Mastering Fraction Operations on the TI-84 Plus Calculator

Delving into the enigmatic world of fractions on the TI-84 Plus calculator could appear to be a frightening job, however worry not! This complete information will equip you with the data and methods to navigate this mathematical realm with ease. Whether or not you are a seasoned math wizard or an aspiring numerical fanatic, this insightful article will illuminate the trail to fraction mastery in your trusty TI-84 Plus.

Initially, let’s break down the fundamentals: fractions are merely numbers expressed as a ratio of two integers. On the TI-84 Plus, you may enter fractions in two methods. As an example, to enter the fraction 1/2, you may both kind “1/2” or “1 ÷ 2.” The calculator will routinely acknowledge the fraction and retailer it internally. Alternatively, you need to use the devoted “Frac” button to transform a decimal into its fractional equal. As soon as you’ve got inputted your fraction, you are able to embark on a world of mathematical potentialities.

The TI-84 Plus gives an array of highly effective features that make working with fractions a breeze. For instance, you may simplify fractions utilizing the “simplify” command, which reduces fractions to their lowest phrases. Moreover, the calculator supplies features for addition, subtraction, multiplication, and division of fractions, permitting you to carry out advanced calculations with ease. And if you might want to convert a fraction to a decimal or share, the TI-84 Plus has you lined with devoted conversion features. By harnessing these capabilities, you can sort out fraction-based issues with confidence and precision.

Coming into Fractions into the TI-84 Plus

Fractions are a vital a part of arithmetic, and the TI-84 Plus calculator makes it straightforward to enter and work with them. There are two predominant methods to enter a fraction into the TI-84 Plus:

1. Utilizing the fraction template: The fraction template is essentially the most easy technique to enter a fraction. To make use of the fraction template, press the "2nd" key adopted by the "x-1" key. This may open up the fraction template, which has three elements: the numerator, the denominator, and the fraction bar.

   • To enter the numerator, use the arrow keys to maneuver the cursor to the numerator subject. Then, use the quantity keys to enter the numerator.
   • To enter the denominator, use the arrow keys to maneuver the cursor to the denominator subject. Then, use the quantity keys to enter the denominator.
   • To enter the fraction bar, press the "enter" key.

   After getting entered the numerator and denominator, the fraction will seem on the display screen. For instance, to enter the fraction 1/2, you’ll press the "2nd" key adopted by the "x-1" key. Then, you’ll use the arrow keys to maneuver the cursor to the numerator subject and press the "1" key. You’ll then use the arrow keys to maneuver the cursor to the denominator subject and press the "2" key. Lastly, you’ll press the "enter" key. The fraction 1/2 would then seem on the display screen.

2. Utilizing the division operator: It’s also possible to enter a fraction into the TI-84 Plus utilizing the division operator. To do that, merely enter the numerator adopted by the division operator (/) adopted by the denominator. For instance, to enter the fraction 1/2 utilizing the division operator, you’ll press the "1" key adopted by the "/" key adopted by the "2" key. The fraction 1/2 would then seem on the display screen.

   Utilizing the division operator to enter a fraction is usually sooner than utilizing the fraction template, however it is very important watch out to not make any errors. Should you make a mistake, the fraction won’t be entered appropriately and you have to to begin over.

Here’s a desk summarizing the 2 strategies for getting into fractions into the TI-84 Plus:

Technique	Steps
Fraction template	1. Press the "2nd" key adopted by the "x-1" key.
	2. Use the arrow keys to maneuver the cursor to the numerator subject.
	3. Enter the numerator utilizing the quantity keys.
	4. Use the arrow keys to maneuver the cursor to the denominator subject.
	5. Enter the denominator utilizing the quantity keys.
	6. Press the "enter" key.
Division operator	1. Enter the numerator.
	2. Press the "/" key.
	3. Enter the denominator.

Utilizing the MATH Menu to Convert Decimals to Fractions

The TI-84 Plus calculator gives a complete MATH menu that features varied instruments for working with fractions. Considered one of these instruments is the "Frac" command, which lets you convert decimals to their equal fractions. This characteristic is especially helpful when coping with rational numbers or performing calculations that contain fractions.

To entry the Frac command, comply with these steps:

1. Make sure that your TI-84 Plus calculator is within the "MATH" mode.
2. Scroll right down to the "Frac" entry within the menu and press "ENTER."

The Frac command requires you to supply the decimal quantity you need to convert to a fraction. Here is easy methods to enter the decimal:

1. After urgent "ENTER," you will notice a blinking cursor on the display screen.
2. Enter the decimal worth as you’ll usually write it, together with the decimal level.
3. Press "ENTER" once more to provoke the conversion.

The TI-84 Plus calculator will carry out the conversion and show the consequence as a fraction. The fraction might be within the easiest kind, which means it will likely be decreased to its lowest phrases. For instance, if you happen to enter the decimal 0.75, the calculator will convert it to the fraction 3/4.

Listed here are some further factors to notice concerning the Frac command:

• The Frac command can solely convert terminating decimals to fractions. Should you enter a non-terminating decimal (like 0.333…), the calculator will show an error message.
• The calculator will routinely cut back the fraction to its easiest kind. You can not specify the specified type of the fraction.
• The Frac command is especially helpful when you might want to convert decimals to fractions for calculations. For instance, if you wish to add 0.25 and 0.5, you need to use the Frac command to transform them to 1/4 and 1/2, respectively, after which carry out the addition as fractions.
• The Frac command will also be used to transform fractions to decimals. To do that, merely enter the fraction as a command, e.g., "Frac(1/2)."

Manipulating Fractions Utilizing the FRAC Command

The FRAC command on the TI-84 Plus calculator is a robust device for working with fractions. It may be used to transform decimals to fractions, simplify fractions, add, subtract, multiply, and divide fractions, and discover the best frequent issue (GCF) and least frequent a number of (LCM) of two or extra fractions.

To make use of the FRAC command, kind the command adopted by the numerator and denominator of the fraction in parentheses. For instance, to enter the fraction 1/2, you’ll kind: FRAC(1,2).

After getting entered a fraction utilizing the FRAC command, you need to use the calculator’s arrow keys to maneuver the cursor across the fraction. The up and down arrow keys transfer the cursor between the numerator and denominator, and the left and proper arrow keys transfer the cursor throughout the numerator or denominator.

It’s also possible to use the calculator’s menu to carry out operations on fractions. To entry the menu, press the [2nd] key adopted by the [MATH] key. The menu will seem on the display screen. Use the arrow keys to maneuver the cursor to the specified operation and press the [ENTER] key.

The next desk summarizes the operations that you may carry out on fractions utilizing the FRAC command:

Operation	Syntax	Instance
Convert a decimal to a fraction	FRAC(decimal)	FRAC(0.5) = 1/2
Simplify a fraction	FRAC(numerator, denominator)	FRAC(3,6) = 1/2
Add fractions	FRAC(numerator1, denominator1) + FRAC(numerator2, denominator2)	FRAC(1,2) + FRAC(1,3) = 5/6
Subtract fractions	FRAC(numerator1, denominator1) – FRAC(numerator2, denominator2)	FRAC(1,2) – FRAC(1,3) = 1/6
Multiply fractions	FRAC(numerator1, denominator1) * FRAC(numerator2, denominator2)	FRAC(1,2) * FRAC(1,3) = 1/6
Divide fractions	FRAC(numerator1, denominator1) / FRAC(numerator2, denominator2)	FRAC(1,2) / FRAC(1,3) = 3/2
Discover the best frequent issue (GCF) of two or extra fractions	GCD(FRAC(numerator1, denominator1), FRAC(numerator2, denominator2))	GCD(FRAC(1,2), FRAC(1,3)) = 1
Discover the least frequent a number of (LCM) of two or extra fractions	LCM(FRAC(numerator1, denominator1), FRAC(numerator2, denominator2))	LCM(FRAC(1,2), FRAC(1,3)) = 6

Including and Subtracting Fractions on the TI-84 Plus

The TI-84 Plus graphing calculator is a robust device that can be utilized to carry out quite a lot of mathematical operations, together with including and subtracting fractions. So as to add or subtract fractions on the TI-84 Plus, comply with these steps:

1. Enter the primary fraction into the calculator. To do that, press the “2nd” button adopted by the “frac” button. This may convey up the Fraction Editor. Enter the numerator of the fraction into the highest subject and the denominator into the underside subject. Press the “enter” button to save lots of the fraction.
2. Enter the second fraction into the calculator. To do that, repeat step 1.
3. So as to add the fractions, press the “+” button. To subtract the fractions, press the “-” button.
4. The results of the operation might be displayed within the calculator’s show. If the result’s a combined quantity, the integer a part of the quantity might be displayed first, adopted by the fraction half. For instance, if you happen to add 1/2 and 1/3, the consequence might be displayed as 5/6.

Here’s a desk summarizing the steps for including and subtracting fractions on the TI-84 Plus:

Operation	Steps
Addition	Enter the primary fraction into the calculator. Enter the second fraction into the calculator. Press the “+” button. The results of the operation might be displayed within the calculator’s show.
Subtraction	Enter the primary fraction into the calculator. Enter the second fraction into the calculator. Press the “-” button. The results of the operation might be displayed within the calculator’s show.

Listed here are some further suggestions for including and subtracting fractions on the TI-84 Plus:

• It’s also possible to use the “math” menu so as to add or subtract fractions. To do that, press the “math” button after which choose the “fractions” possibility. This may convey up a menu of choices for working with fractions, together with including, subtracting, multiplying, and dividing fractions.
• In case you are working with a fancy fraction, you need to use the “advanced” menu to enter the fraction. To do that, press the “advanced” button after which choose the “fraction” possibility. This may convey up a menu of choices for working with advanced fractions, together with including, subtracting, multiplying, and dividing advanced fractions.
• The TI-84 Plus will also be used to simplify fractions. To do that, press the “math” button after which choose the “simplify” possibility. This may convey up a menu of choices for simplifying fractions, together with simplifying fractions to their lowest phrases, simplifying fractions to combined numbers, and simplifying fractions to decimals.

Multiplying and Dividing Fractions on the TI-84 Plus

Coming into Fractions

To enter a fraction into the TI-84 Plus, use the fraction template:

(numerator / denominator)

For instance, to enter the fraction 1/2, kind:

(1 / 2)

Multiplying Fractions

To multiply fractions on the TI-84 Plus, use the asterisk (*) key.

(numerator1 / denominator1) * (numerator2 / denominator2)

For instance, to multiply 1/2 by 3/4, kind:

(1 / 2) * (3 / 4)

The consequence might be 3/8.

Dividing Fractions

To divide fractions on the TI-84 Plus, use the ahead slash (/) key.

(numerator1 / denominator1) / (numerator2 / denominator2)

For instance, to divide 1/2 by 3/4, kind:

(1 / 2) / (3 / 4)

The consequence might be 2/3.

Changing Blended Numbers to Improper Fractions

To transform a combined quantity to an improper fraction on the TI-84 Plus, use the next steps:

1. Multiply the entire quantity by the denominator of the fraction.
2. Add the numerator of the fraction to the results of step 1.
3. Place the results of step 2 over the denominator of the fraction.

For instance, to transform the combined quantity 2 1/3 to an improper fraction, kind:

(2 * 3) + 1 / 3

The consequence might be 7/3.

Changing Improper Fractions to Blended Numbers

To transform an improper fraction to a combined quantity on the TI-84 Plus, use the next steps:

1. Divide the numerator by the denominator.
2. The quotient of step 1 is the entire quantity.
3. The rest of step 1 is the numerator of the fraction.
4. The denominator of the fraction is similar because the denominator of the improper fraction.

For instance, to transform the improper fraction 7/3 to a combined quantity, kind:

7 / 3

The consequence might be 2 1/3.

Observe Issues

1. Multiply the fractions 1/2 and three/4.
2. Divide the fractions 1/2 by 3/4.
3. Convert the combined quantity 2 1/3 to an improper fraction.
4. Convert the improper fraction 7/3 to a combined quantity.
5. Simplify the fraction 12x^2 / 15x.

Reply Key:

1. 3/8
2. 2/3
3. 7/3
4. 2 1/3
5. 4x

Changing Fractions to Blended Numbers

Changing fractions to combined numbers is crucial for performing varied mathematical operations. A combined quantity is a mix of a complete quantity and a fraction, representing a worth higher than 1. To transform a fraction to a combined quantity, comply with these steps:

1. Divide the numerator (prime quantity) by the denominator (backside quantity) utilizing lengthy division.

2. The quotient obtained from the division represents the entire quantity a part of the combined quantity.

3. The rest from the division turns into the numerator of the fraction a part of the combined quantity.

4. The denominator stays the identical as the unique fraction.

For instance, to transform the fraction 7/3 to a combined quantity:

3 ) 7

3 2

6

1

Due to this fact, 7/3 as a combined quantity is 2 1/3.

7. Changing Improper Fractions to Blended Numbers

An improper fraction is a fraction the place the numerator is larger than or equal to the denominator. To transform an improper fraction to a combined quantity, comply with these steps:

1. Divide the numerator by the denominator utilizing lengthy division.
2. The quotient obtained from the division represents the entire quantity a part of the combined quantity.
3. The rest from the division turns into the numerator of the fraction a part of the combined quantity.
4. The denominator stays the identical as the unique fraction.

Instance:

Convert the improper fraction 11/4 to a combined quantity:

4 ) 11

4 8

8

3

Due to this fact, 11/4 as a combined quantity is 2 3/4.

Changing Blended Numbers to Fractions

Changing combined numbers to fractions includes two steps:

1. Multiply the entire quantity by the denominator of the fraction

For instance, if you wish to convert 3 1/2 to a fraction, you’ll multiply 3 by 2 (the denominator of the fraction 1/2) to get 6.

2. Add the numerator of the fraction to the consequence

Lastly, add the numerator of the fraction (1) to the results of the multiplication (6) to get 7. The fraction equal of three 1/2 is due to this fact 7/2.

Instance

Let’s convert 4 3/4 to a fraction.

1. Multiply the entire quantity (4) by the denominator of the fraction (4) to get 16.
2. Add the numerator of the fraction (3) to the results of the multiplication (16) to get 19.

Due to this fact, 4 3/4 is equal to the fraction 19/4.

Changing Fractions to Blended Numbers

Changing fractions to combined numbers will be achieved by utilizing the next steps:

1. Divide the denominator of the fraction into the numerator

For instance, if you wish to convert the fraction 7/2 to a combined quantity, you’ll divide 2 into 7 to get 3 because the quotient.

2. The rest of the division is the numerator of the fraction a part of the combined quantity

On this case, there is no such thing as a the rest, so the fraction a part of the combined quantity could be 0/2, which will be simplified to only 0.

3. The quotient of the division is the entire quantity a part of the combined quantity

Due to this fact, 7/2 is equal to the combined quantity 3.

Instance

Let’s convert 19/4 to a combined quantity.

1. Divide the denominator (4) into the numerator (19) to get 4 because the quotient and three as the rest.
2. The rest (3) is the numerator of the fraction a part of the combined quantity, and the quotient (4) is the entire quantity a part of the combined quantity.

Due to this fact, 19/4 is equal to the combined quantity 4 3/4.

Desk of Conversions

The next desk exhibits the conversions for some frequent fractions and combined numbers:

Blended Quantity	Fraction
3 1/2	7/2
4 3/4	19/4
2 1/3	7/3
1 3/8	11/8
5 2/5	27/5

Discovering Least Frequent Multiples and Denominators

The Least Frequent A number of (LCM) of two or extra fractions is the smallest optimistic integer that’s divisible by all of the denominators of the given fractions. The Least Frequent Denominator (LCD) of two or extra fractions is the smallest optimistic integer that every one the denominators of the given fractions divide into evenly. Here is easy methods to discover the LCM and LCD utilizing the TI-84 Plus calculator:

Discovering the Least Frequent A number of (LCM) utilizing TI-84 Plus

1. Enter the numerators and denominators of the fractions into the calculator. For instance, if you wish to discover the LCM of 1/2 and 1/3, enter 1/2 and 1/3 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “lcm()” operate.
3. Kind the fractions you entered in Step 1 as arguments to the “lcm()” operate, separating them with a comma. For instance, kind lcm(1/2, 1/3).
4. Press the “enter” button.
5. The calculator will show the LCM of the fractions.

Discovering the Least Frequent Denominator (LCD) utilizing TI-84 Plus

1. Enter the numerators and denominators of the fractions into the calculator. For instance, if you wish to discover the LCD of 1/2 and 1/3, enter 1/2 and 1/3 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “liquid crystal display()” operate.
3. Kind the fractions you entered in Step 1 as arguments to the “liquid crystal display()” operate, separating them with a comma. For instance, kind liquid crystal display(1/2, 1/3).
4. Press the “enter” button.
5. The calculator will show the LCD of the fractions.

Instance

Discover the LCM and LCD of 1/2, 1/3, and 1/4.

LCM:

1. Enter 1/2, 1/3, and 1/4 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “lcm()” operate.
3. Kind lcm(1/2, 1/3, 1/4) into the calculator.
4. Press the “enter” button.
5. The calculator shows 6, which is the LCM of 1/2, 1/3, and 1/4.

LCD:

1. Enter 1/2, 1/3, and 1/4 into the calculator.
2. Press the “2nd” button, then press the “x-1” button to entry the “liquid crystal display()” operate.
3. Kind liquid crystal display(1/2, 1/3, 1/4) into the calculator.
4. Press the “enter” button.
5. The calculator shows 12, which is the LCD of 1/2, 1/3, and 1/4.

Extra Examples

Fraction 1	Fraction 2	LCM	LCD
1/2	1/3	6	6
1/3	1/4	12	12
1/4	1/5	20	20
1/2	1/3	1/4	12

Evaluating and Ordering Fractions

To check and order fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “>” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show “1” if the primary fraction is larger than the second fraction, “0” if the primary fraction is lower than the second fraction, or “ERROR” if the fractions are equal.

It’s also possible to use the “>” and “<” keys to match and order fractions in an inventory.

1. Enter the fractions into the calculator in an inventory.
2. Press the “STAT” key.
3. Choose the “EDIT” menu.
4. Choose the “Type” submenu.
5. Choose the “Ascending” or “Descending” possibility.
6. Press the “ENTER” key.

The calculator will type the fractions in ascending or descending order.

Changing Fractions to Decimals

To transform a fraction to a decimal on the TI-84 Plus calculator, comply with these steps:

1. Enter the fraction into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Dec” submenu.
5. Press the “ENTER” key.

The calculator will show the decimal illustration of the fraction.

Changing Decimals to Fractions

To transform a decimal to a fraction on the TI-84 Plus calculator, comply with these steps:

1. Enter the decimal into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Frac” submenu.
5. Press the “ENTER” key.

The calculator will show the fraction illustration of the decimal.

Including and Subtracting Fractions

So as to add or subtract fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “+” or “-” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show the sum or distinction of the fractions.

Multiplying and Dividing Fractions

To multiply or divide fractions on the TI-84 Plus calculator, comply with these steps:

1. Enter the primary fraction into the calculator.
2. Press the “*” or “/” key.
3. Enter the second fraction.
4. Press the “ENTER” key.

The calculator will show the product or quotient of the fractions.

Simplifying Fractions

To simplify a fraction on the TI-84 Plus calculator, comply with these steps:

1. Enter the fraction into the calculator.
2. Press the “MATH” key.
3. Choose the “FRAC” menu.
4. Choose the “Simp” submenu.
5. Press the “ENTER” key.

The calculator will show the simplified fraction.

Utilizing Fractions in Equations

You should utilize fractions in equations on the TI-84 Plus calculator. For instance, to resolve the equation 1/2x + 1/4 = 1/8, you’ll enter the next into the calculator:

1/2x + 1/4 = 1/8
clear up(1/2x + 1/4 = 1/8, x)

The calculator would show the answer x = 1/2.

Fraction	Decimal	Simplified Fraction
1/2	0.5	1/2
1/4	0.25	1/4
1/8	0.125	1/8
3/4	0.75	3/4
5/8	0.625	5/8

Fixing Equations Involving Fractions

Here is a step-by-step information on easy methods to clear up equations involving fractions on the TI-84 Plus calculator:

1. Simplify the equation

Begin by simplifying the equation as a lot as potential. This may increasingly contain multiplying or dividing each side by the identical quantity to do away with fractions, or combining like phrases.

2. Multiply each side by the LCD

The least frequent denominator (LCD) of the fractions within the equation is the smallest quantity that’s divisible by the entire denominators. Multiply each side of the equation by the LCD to do away with the fractions.

3. Resolve the ensuing equation

After getting multiplied each side by the LCD, you’ll have a brand new equation that now not incorporates fractions. Resolve this equation utilizing the same old strategies for fixing equations.

4. Examine your answer

After getting discovered an answer to the equation, test your answer by plugging it again into the unique equation. If the equation holds true, then your answer is right.

Instance:

Resolve the equation 1/2x + 1/4 = 1/3.

1. Simplify the equation

12(1/2x + 1/4) = 12(1/3)

6x + 3 = 4

2. Multiply each side by the LCD

6x = 1

3. Resolve the ensuing equation

x = 1/6

4. Examine your answer

1/2(1/6) + 1/4 = 1/3

1/12 + 1/4 = 1/3

4/12 + 3/12 = 1/3

7/12 = 1/3

Extra Suggestions

– When multiplying fractions, multiply the numerators and multiply the denominators.

– When dividing fractions, invert the second fraction and multiply.

– The LCD will be discovered by discovering the least frequent a number of (LCM) of the denominators.

– Watch out to not divide by zero.

Utilizing Fractions to Resolve Phrase Issues

Fractions are a standard a part of on a regular basis life. We use them to explain parts of meals, time, and distance. When fixing phrase issues involving fractions, it is very important perceive the ideas of numerators, denominators, and equal fractions.

Numerators symbolize the variety of elements being thought-about, whereas denominators symbolize the full variety of elements into which an entire is split. Equal fractions are fractions that symbolize the identical worth, regardless that they’ve completely different numerators and denominators.

For instance, the fractions 1/2, 2/4, and three/6 are all equal as a result of they symbolize the identical worth, which is half of a complete.

When fixing phrase issues involving fractions, comply with these steps:

1. Learn the issue rigorously. Decide what data is being offered and what data is being requested for.
2. Establish the fractions in the issue. Decide the numerators and denominators of every fraction.
3. Convert any combined numbers to improper fractions. A combined quantity is a quantity that has an entire quantity half and a fraction half. To transform a combined quantity to an improper fraction, multiply the entire quantity half by the denominator of the fraction half after which add the numerator of the fraction half. The result’s the numerator of the improper fraction, and the denominator is similar because the denominator of the unique fraction.
4. Discover the least frequent a number of (LCM) of the denominators. The LCM is the smallest quantity that’s divisible by the entire denominators. To search out the LCM, listing the prime elements of every denominator after which multiply the very best energy of every prime issue that seems in any of the denominators.
5. Convert all of the fractions to equal fractions with the LCM because the denominator. To do that, multiply the numerator and denominator of every fraction by the suitable issue.
6. Carry out the operation(s) indicated by the issue. This may increasingly contain including, subtracting, multiplying, or dividing fractions.
7. Simplify the consequence. Cut back the fraction to its lowest phrases by dividing the numerator and denominator by their best frequent issue (GCF). Specific the consequence as a combined quantity if applicable.

Instance:

A recipe for chocolate chip cookies calls for two 1/2 cups of flour. Should you solely have 3/4 of a cup of flour, what fraction of the recipe are you able to make?

Answer:

1. Learn the issue rigorously. You’re given that you’ve 3/4 of a cup of flour and you might want to decide what fraction of the recipe you may make.
2. Establish the fractions in the issue. The fraction 2 1/2 is equal to the improper fraction 5/2, and the fraction 3/4 is equal to the improper fraction 3/4.
3. Convert the combined quantity to an improper fraction. 5/2
4. Discover the least frequent a number of (LCM) of the denominators. The LCM of two and 4 is 4.
5. Convert all of the fractions to equal fractions with the LCM because the denominator. 5/2 x 2/2 = 10/4 and three/4 x 1/1 = 3/4
6. Carry out the operation indicated by the issue. 10/4 – 3/4 = 7/4
7. Simplify the consequence. 7/4

Due to this fact, you may make 7/4 of the recipe with 3/4 of a cup of flour.

Extra Suggestions:

• When including or subtracting fractions, ensure that the fractions have the identical denominator.
• When multiplying fractions, multiply the numerators and multiply the denominators.
• When dividing fractions, invert the divisor and multiply.
• Do not be afraid to make use of a calculator to test your solutions.

Evaluating Numerical Expressions with Fractions

The TI-84 Plus calculator can be utilized to guage numerical expressions involving fractions. To do that, you need to use the next steps:

1. Enter the numerator of the fraction into the calculator.
2. Press the “หาร” (÷) key.
3. Enter the denominator of the fraction into the calculator.
4. Press the “ENTER” key.

For instance, to guage the expression 1/2, you’ll enter the next into the calculator:

1÷2

and press the “ENTER” key. The calculator would then show the consequence, which is 0.5.

Utilizing the Ans Variable

It’s also possible to use the Ans variable to retailer the results of a earlier calculation. This may be helpful if you wish to use the results of one calculation in a subsequent calculation.

To retailer the results of a calculation within the Ans variable, merely press the “STORE” key after the calculation is full. For instance, to retailer the results of the expression 1/2 within the Ans variable, you’ll enter the next into the calculator:

1÷2STORE÷

The Ans variable can then be utilized in subsequent calculations by merely getting into its title. For instance, to calculate the expression 1/2 + 1/4, you’ll enter the next into the calculator:

Ans+1÷4

Utilizing the Fraction Key

The TI-84 Plus calculator additionally has a devoted fraction key, which can be utilized to enter fractions straight into the calculator.

To enter a fraction utilizing the fraction key, press the “ALPHA” key adopted by the “x-1” key. The calculator will then show a fraction template. Enter the numerator of the fraction into the highest field and the denominator of the fraction into the underside field. Press the “ENTER” key to enter the fraction into the calculator.

For instance, to enter the fraction 1/2 into the calculator, you’ll press the next keys:

ALPHAx-11ENTER2ENTER

Evaluating Extra Complicated Expressions

The TI-84 Plus calculator will also be used to guage extra advanced expressions involving fractions. For instance, to guage the expression (1/2) + (1/4), you’ll enter the next into the calculator:

(

1÷2)+(1÷4)

The calculator would then show the consequence, which is 3/4.

Desk of Examples

Expression	Calculator Enter	Outcome
1/2	1 ÷ 2	0.5
1/2 + 1/4	(1 ÷ 2) + (1 ÷ 4)	0.75
(1/2) * (1/4)	(1 ÷ 2) * (1 ÷ 4)	0.125
1/(1/2)	1 ÷ (1 ÷ 2)	2

Discovering Important Factors of Features Involving Fractions

Important factors are factors the place the primary by-product of a operate is both zero or undefined. To search out the essential factors of a operate involving fractions, we are able to use the quotient rule.

The quotient rule states that if we’ve a operate of the shape $f(x) = frac{p(x)}{q(x)}$, the place $p(x)$ and $q(x)$ are polynomials, then the by-product of $f(x)$ is given by:

$$f'(x) = frac{q(x)p'(x) – p(x)q'(x)}{q(x)^2}$$

Utilizing this rule, we are able to discover the essential factors of any operate involving fractions.

Instance

Discover the essential factors of the operate $f(x) = frac{x^2+1}{x-1}$.

Utilizing the quotient rule, we discover that:

$$f'(x) = frac{(x-1)(2x) – (x^2+1)(1)}{(x-1)^2} = frac{2x^2 – 2x – x^2 – 1}{(x-1)^2} = frac{x^2 – 2x – 1}{(x-1)^2}$$

The essential factors are the factors the place $f'(x) = 0$ or $f'(x)$ is undefined.

To search out the place $f'(x) = 0$, we clear up the equation $x^2 – 2x – 1 = 0$. This equation elements as $(x-1)(x+1) = 0$, so the options are $x = 1$ and $x = -1$.

To search out the place $f'(x)$ is undefined, we set the denominator of $f'(x)$ equal to zero. This offers us $(x-1)^2 = 0$, so the one answer is $x = 1$.

Due to this fact, the essential factors of $f(x) = frac{x^2+1}{x-1}$ are $x = 1$ and $x = -1$.

Common Process

To search out the essential factors of a operate involving fractions, we are able to comply with these steps:

1. Discover the by-product of the operate utilizing the quotient rule.
2. Set the by-product equal to zero and clear up for $x$.
3. Set the denominator of the by-product equal to zero and clear up for $x$.
4. The essential factors are the factors the place the by-product is zero or undefined.

Extra Notes

* If the denominator of the operate is a continuing, then the operate won’t have any essential factors.
* If the numerator of the operate is a continuing, then the operate may have a essential level at $x = 0$.
* If the operate is undefined at a degree, then that time isn’t a essential level.

Utilizing Derivatives to Analyze Features with Fractions

The by-product of a operate is a measure of its charge of change. It may be used to research the operate’s habits, together with its essential factors, maxima, and minima.

When coping with features that comprise fractions, it is very important keep in mind that the by-product of a quotient is the same as the numerator instances the by-product of the denominator minus the denominator instances the by-product of the numerator, all divided by the sq. of the denominator.

$$ frac{d}{dx} left[ frac{f(x)}{g(x)} right] = frac{g(x)f'(x) – f(x)g'(x)}{g(x)^2} $$

This rule can be utilized to search out the by-product of any operate that incorporates a fraction. For instance, the by-product of the operate

$$ f(x) = frac{x^2 + 1}{x-1} $$

is

$$ f'(x) = frac{(x-1)(2x) – (x^2 + 1)(1)}{(x-1)^2} = frac{2x^2 – 2x – x^2 – 1}{(x-1)^2} = frac{x^2 – 2x – 1}{(x-1)^2} $$

This by-product can be utilized to research the operate’s habits. For instance, the by-product is the same as zero on the factors x = 1 and x = -1/2. These factors are the essential factors of the operate.

The by-product is optimistic for x > 1 and x < -1/2. Which means that the operate is growing on these intervals. The by-product is detrimental for -1/2 < x < 1. Which means that the operate is reducing on this interval.

The operate has a most on the level x = 1 and a minimal on the level x = -1/2. These factors will be discovered by discovering the essential factors after which evaluating the operate at these factors.

The by-product will also be used to search out the concavity of the operate. The operate is concave up on the intervals (-∞, -1/2) and (1, ∞). The operate is concave down on the interval (-1/2, 1).

The concavity of the operate can be utilized to find out the operate’s form. A operate that’s concave up is a parabola that opens up. A operate that’s concave down is a parabola that opens down.

The by-product is a robust device that can be utilized to research the habits of features. When coping with features that comprise fractions, it is very important bear in mind the quotient rule for derivatives.

Instance

Discover the by-product of the operate

$$ f(x) = frac{x^3 + 2x^2 – 1}{x^2 – 1} $$

Utilizing the quotient rule, we’ve

$$ f'(x) = frac{(x^2 – 1)(3x^2 + 4x) – (x^3 + 2x^2 – 1)(2x)}{(x^2 – 1)^2} $$

$$ = frac{3x^4 + 4x^3 – 3x^2 – 4x – 2x^4 – 4x^3 + 4x^2 + 2x}{(x^2 – 1)^2} $$

$$ = frac{x^4}{(x^2 – 1)^2} $$

The by-product of the operate is

$$ f'(x) = frac{x^4}{(x^2 – 1)^2} $$

Utilizing Integrals to Discover the Space Beneath a Curve Involving Fractions

1. Outline the Operate

Start by getting into the operate involving fractions into the TI-84 Plus. As an example, to enter the operate f(x) = (x+2)/(x-1), press the next keys:

1. MODE
2. FUNC
3. Y=
4. Enter (x+2)/(x-1)

2. Set the Graph Window

Modify the graph window to show the related portion of the curve. To do that, press the WINDOW button and enter applicable values for Xmin, Xmax, Ymin, and Ymax.

For instance, to set the window to show the curve from x=-5 to x=5 and y=-10 to y=10, enter the next values:

Setting	Worth
Xmin	-5
Xmax	5
Ymin	-10
Ymax	10

3. Discover the Roots of the Denominator

To arrange for integration, you might want to discover the roots of the denominator of the operate. On this instance, the denominator is x-1. Press the CALC button, choose ZERO, then select ZERO once more. Use the arrow keys to maneuver the cursor to the zero level of the operate and press ENTER.

4. Use the Integration Characteristic

After getting outlined the operate and set the suitable window, you need to use the combination characteristic to search out the realm underneath the curve. Press the MATH button, choose NUMERICAL, after which select ∫f(x)dx.

5. Specify the Bounds of Integration

Enter the decrease and higher bounds of integration. As an example, to search out the realm underneath the curve from x=0 to x=3, enter 0 because the decrease sure and 3 because the higher sure.

6. Calculate the Integral

Press ENTER to calculate the integral worth, which represents the realm underneath the curve throughout the specified bounds.

7. Resolve Indeterminate Kinds

If the integral result’s an indeterminate kind resembling ∞, -∞, or 0/0, you have to to analyze the habits of the operate close to the purpose of discontinuity. Use restrict analysis methods or graphing to find out the suitable worth.

17. Instance: Discovering the Space Beneath a Hyperbola

Let’s discover the realm underneath the hyperbola f(x) = (x-1)/(x+1) from x=0 to x=2 utilizing the TI-84 Plus.

Steps:

• Enter the operate: y1=(x-1)/(x+1)
• Set the graph window: Xmin=-5, Xmax=5, Ymin=-5, Ymax=5
• Discover the basis of the denominator: x=-1
• Combine the operate:
  1. MATH
  2. NUMERICAL
  3. ∫f(x)dx
  4. 0, 2
• Outcome: ln(3) ≈ 1.0986

Find out how to Calculate Limits of Features with Fractions on TI-84 Plus

The TI-84 Plus calculator can be utilized to calculate limits of features, together with features that comprise fractions. To calculate the restrict of a operate with a fraction, comply with these steps:

1. Enter the operate into the calculator.
2. Press the “CALC” button.
3. Choose the “restrict” possibility.
4. Enter the worth of the variable at which you need to calculate the restrict.
5. Press the “ENTER” button.

The calculator will show the restrict of the operate on the given worth of the variable.

For instance, to calculate the restrict of the operate f(x) = (x^2 – 1) / (x – 1) at x = 1, comply with these steps:

1. Enter the operate into the calculator: f(x) = (x^2 – 1) / (x – 1)
2. Press the “CALC” button.
3. Choose the “restrict” possibility.
4. Enter the worth of x at which you need to calculate the restrict: x = 1
5. Press the “ENTER” button.

The calculator will show the restrict of the operate at x = 1, which is 2.

Instance: Calculating the Restrict of a Rational Operate

Contemplate the rational operate:

“`
f(x) = (x^2 – 4) / (x – 2)
“`

To search out the restrict of this operate as x approaches 2, we are able to use the TI-84 Plus calculator.

Step 1: Enter the operate into the calculator.

“`
f(x) = (x^2 – 4) / (x – 2)
“`

Step 2: Press the “CALC” button.

Step 3: Choose the “restrict” possibility.

Step 4: Enter the worth of x at which you need to calculate the restrict.

“`
x = 2
“`

Step 5: Press the “ENTER” button.

The calculator will show the restrict of the operate as x approaches 2, which is 4.

Enter	Output
f(x) = (x^2 – 4) / (x – 2)	4

Extra Notes

When calculating limits of features with fractions, it is very important word the next:

* The restrict of a fraction is the same as the restrict of the numerator divided by the restrict of the denominator, offered that the denominator doesn’t method zero.
* If the denominator of a fraction approaches zero, the restrict of the fraction could also be indeterminate. On this case, chances are you’ll want to make use of different methods to guage the restrict.
* It’s all the time a good suggestion to simplify fractions earlier than calculating limits. This can assist to keep away from potential errors.

Dealing with Continuity of Features with Fractions

Manipulating fractions on the TI-84 Plus calculator empowers us to discover the habits of features containing fractions and assess their continuity. Features carrying fractions could possess discontinuities, factors the place the operate experiences abrupt interruptions or “jumps.” These discontinuities can come up as a result of specific nature of the fraction, resembling division by zero or undefined expressions.

To find out the continuity of a operate involving fractions, we should scrutinize the operate’s habits at essential factors the place the denominator of the fraction approaches zero or turns into undefined. If the operate’s restrict at that time coincides with the operate’s worth at that time, then the operate is taken into account steady at that time. In any other case, a discontinuity exists.

Detachable Discontinuities

In sure circumstances, discontinuities will be “eliminated” by simplifying or redefining the operate. As an example, think about the operate:

f(x) = (x-2)/(x^2-4)

The denominator, (x^2-4), approaches zero at x = 2 and x = -2. Nevertheless, these factors aren’t detachable discontinuities as a result of the restrict of the operate as x approaches both of those factors doesn’t match the operate’s worth at these factors.

Level	Restrict	Operate Worth	Discontinuity Kind
x = 2	1/4	Undefined	Important Discontinuity
x = -2	-1/4	Undefined	Important Discontinuity

Important Discontinuities: Factors the place the restrict of the operate doesn’t exist or is infinite, making the discontinuity “important” or irremovable.

Instance: Figuring out Discontinuities

Let’s study the operate:

g(x) = (x^2-9)/(x-3)

The denominator, (x-3), approaches zero at x = 3. Substituting x = 3 into the operate yields an undefined expression, indicating a possible discontinuity.

To find out the kind of discontinuity, we calculate the restrict of the operate as x approaches 3:

lim (x->3) (x^2-9)/(x-3) = lim (x->3) [(x+3)(x-3)]/(x-3) = lim (x->3) x+3 = 6

Because the restrict (6) doesn’t coincide with the operate’s worth at x = 3 (undefined), the discontinuity is crucial and can’t be eliminated.

Abstract of Continuity Circumstances

To find out the continuity of a operate involving fractions:

1. Issue the denominator to determine potential discontinuities.
2. Substitute the potential discontinuity into the operate to test for an undefined expression.
3. If an undefined expression is discovered, calculate the restrict of the operate as x approaches the potential discontinuity.
4. If the restrict exists and equals the operate’s worth at that time, the discontinuity is detachable.
5. If the restrict doesn’t exist or doesn’t equal the operate’s worth at that time, the discontinuity is crucial.

Derivatives of Features with Fractions

The by-product of a fraction is discovered utilizing the quotient rule, which states that the by-product of $\frac{f\left(x\right)}{g\left(x\right)}$ is given by:

$f^{\prime }\left(x\right)g\left(x\right)-f\left(x\right)g^{\prime }\left(x\right)={\left(g\left(x\right)\right)}^2$

The place $f^{\prime }\left(x\right)$ and $g^{\prime }\left(x\right)$ symbolize the derivatives of $f\left(x\right)$ and $g\left(x\right)$, respectively.

22. Instance

Discover the by-product of $f\left(x\right)=\frac{x+1}{x-2}$.

Answer:

Utilizing the quotient rule, we’ve:

$f^{\prime }\left(x\right)=\frac{(x-2)\left(1\right)-(x+1)\left(1\right)}{(x-2{)}^2}$

$=\frac{x-2-x-1}{(x-2{)}^2}$

$=\frac{-3}{(x-2{)}^2}$

Due to this fact, $f^{\prime }\left(x\right)=\frac{-3}{(x-2{)}^2}$.

The next desk supplies further examples of derivatives of features with fractions:

Operate	By-product
$\frac{x+2}{x-1}$	$\frac{(x-1)\left(1\right)-(x+2)\left(1\right)}{(x-1{)}^2}$ $=\frac{x-1-x-2}{(x-1{)}^2}$ $=\frac{-3}{(x-1{)}^2}$
$\frac{2x-1}{x+3}$	$\frac{(x+3)\left(2\right)-(2x-1)\left(1\right)}{(x+3{)}^2}$ $=\frac{2x+6-2x+1}{(x+3{)}^2}$ Integrals of Fractions: Partial Fraction Decomposition As a way to discover the indefinite integral of a fraction, we are able to use a way known as partial fraction decomposition. This includes breaking down the fraction into easier fractions that may be built-in extra simply. For instance, think about the next fraction: $$frac{x^2+2x+1}{x^2-1}$$ We will issue the denominator as: $$x^2-1=(x+1)(x-1)$$ So, we are able to decompose the fraction as follows: $$frac{x^2+2x+1}{x^2-1}=frac{A}{x+1}+frac{B}{x-1}$$ the place A and B are constants that we have to clear up for. To search out A, we multiply each side of the equation by x+1: $$x^2+2x+1=A(x-1)+B(x+1)$$ Setting x=-1, we get: $$1=2ARightarrow A=frac{1}{2}$$ To search out B, we multiply each side of the equation by x-1: $$x^2+2x+1=A(x-1)+B(x+1)$$ Setting x=1, we get: $$3=2BRightarrow B=frac{3}{2}$$ Due to this fact, we’ve: $$frac{x^2+2x+1}{x^2-1}=frac{1}{2(x+1)}+frac{3}{2(x-1)}$$ Now, we are able to combine every of those fractions individually: $$intfrac{x^2+2x+1}{x^2-1}dx=frac{1}{2}intfrac{1}{x+1}dx+frac{3}{2}intfrac{1}{x-1}dx$$ Utilizing the ability rule of integration, we get: $$intfrac{x^2+2x+1}{x^2-1}dx=frac{1}{2}ln|x+1|+frac{3}{2}ln|x-1|+C$$ the place C is the fixed of integration. Integration by Substitution One other methodology that can be utilized to search out the indefinite integral of a fraction is integration by substitution. This includes making a substitution for part of the integrand that ends in a less complicated expression. For instance, think about the next fraction: $$frac{1}{x^2+1}$$ We will make the substitution u=x^2+1, which provides us: $$du=2xdx$$ Substituting into the integral, we get: $$intfrac{1}{x^2+1}dx=frac{1}{2}intfrac{1}{u}du$$ Now, we are able to use the ability rule of integration to get: $$intfrac{1}{x^2+1}dx=frac{1}{2}ln|u|+C$$ Substituting again for u, we get: $$intfrac{1}{x^2+1}dx=frac{1}{2}ln|x^2+1|+C$$ the place C is the fixed of integration. Integration by Elements Integration by elements is a way that can be utilized to search out the indefinite integral of a product of two features. This includes discovering two features, u and dv, such that: $$du=v’dxqquadtext{and}qquad dv=udx$$ after which integrating by elements utilizing the next components: $$int udv=uv-int vdu$$ For instance, think about the next fraction: $$frac{x}{x^2+1}$$ We will select u=x and dv=1/(x^2+1)dx, which provides us: $$du=dxqquadtext{and}qquad dv=frac{1}{x^2+1}dx$$ Substituting into the components for integration by elements, we get: $$intfrac{x}{x^2+1}dx=xfrac{1}{x^2+1}-intfrac{1}{x^2+1}dx$$ Now, we are able to use the ability rule of integration to get: $$intfrac{x}{x^2+1}dx=xfrac{1}{x^2+1}-tan^{-1}x+C$$ the place C is the fixed of integration. Examples Listed here are some examples of easy methods to discover the indefinite integral of a fraction utilizing the varied methods mentioned above: Instance 1: Discover the indefinite integral of the next fraction: $$frac{x^2+1}{x^3-1}$$ We will use partial fraction decomposition to interrupt down the fraction as follows: $$frac{x^2+1}{x^3-1}=frac{A}{x-1}+frac{Bx+C}{x^2+x+1}$$ Multiplying each side by x^3-1, we get: $$x^2+1=A(x^2+x+1)+(Bx+C)(x-1)$$ Setting x=1, we get: $$2=A(3)Rightarrow A=frac{2}{3}$$ Setting x=0, we get: $$1=CRightarrow C=1$$ Equating coefficients of x, we get: $$1=A+BRightarrow B=-1/3$$ Due to this fact, we’ve: $$frac{x^2+1}{x^3-1}=frac{2/3}{x-1}-frac{x/3+1}{x^2+x+1}$$ Now, we are able to combine every of those fractions individually: $$intfrac{x^2+1}{x^3-1}dx=frac{2/3}intfrac{1}{x-1}dx-frac{1/3}intfrac{x}{x^2+x+1}dx-intfrac{1}{x^2+x+1}dx$$ Utilizing the ability rule of integration and the arctangent operate, we get: $$intfrac{x^2+1}{x^3-1}dx=frac{2/3}ln|x-1|-frac{1}{6}ln|x^2+x+1|-tan^{-1}x+C$$ the place C is the fixed of integration. Instance 2: Discover the indefinite integral of the next fraction: $$frac{1}{sqrt{x^2+1}}$$ We will use integration by substitution to search out the indefinite integral of this fraction. Let u=x^2+1, then du=2xdx. Substituting into the integral, we get: $$intfrac{1}{sqrt{x^2+1}}dx=intfrac{1}{sqrt{u}}frac{1}{2x}du=frac{1}{2}intfrac{1}{sqrt{u}}du$$ Now, we are able to use the ability rule of integration to get: $$intfrac{1}{sqrt{x^2+1}}dx=frac{1}{2}cdot 2sqrt{u}+C=sqrt{x^2+1}+C$$ the place C is the fixed of integration. Instance 3: Discover the indefinite integral of the next fraction: $$frac{e^x}{x^2+1}$$ We will use integration by elements to search out the indefinite integral of this fraction. Let u=e^x and dv=1/(x^2+1)dx. Then du=e^xdx and v=arctan(x). Substituting into the components for integration by elements, we get: $$intfrac{e^x}{x^2+1}dx=e^xarctan(x)-intarctan(x)e^xdx$$ Now, we are able to use integration by elements once more on the second time period to get: $$intfrac{e^x}{x^2+1}dx=e^xarctan(x)-arctan(x)e^x+intfrac{e^x}{x^ Purposes of Fractions in Physics Resistance in Parallel Circuits When resistors are linked in parallel, the full resistance is lower than the resistance of any particular person resistor. The components for the full resistance in parallel is: “` 1/R_total = 1/R_1 + 1/R_2 + … + 1/R_n “` the place R_1, R_2, …, R_n are the resistances of the person resistors. Capacitance in Parallel Circuits When capacitors are linked in parallel, the full capacitance is the same as the sum of the person capacitances. The components for the full capacitance in parallel is: “` C_total = C_1 + C_2 + … + C_n “` the place C_1, C_2, …, C_n are the capacitances of the person capacitors. Inductance in Sequence Circuits When inductors are linked in collection, the full inductance is the same as the sum of the person inductances. The components for the full inductance in collection is: “` L_total = L_1 + L_2 + … + L_n “` the place L_1, L_2, …, L_n are the inductances of the person inductors. Frequency of a Pendulum The frequency of a pendulum is inversely proportional to the sq. root of its size. The components for the frequency of a pendulum is: “` f = 1/(2π)√(L/g) “` the place f is the frequency, L is the size of the pendulum, and g is the acceleration because of gravity. Projectile Movement The trajectory of a projectile is parabolic. The horizontal and vertical parts of the projectile’s velocity are: “` v_x = v_0 cos(θ) v_y = v_0 sin(θ) – gt “` the place v_0 is the preliminary velocity, θ is the angle of projection, g is the acceleration because of gravity, and t is the time. Work Completed by a Drive The work achieved by a drive over a distance is the same as the product of the drive and the space moved within the course of the drive. The components for the work achieved by a drive is: “` W = Fd cos(θ) “` the place W is the work achieved, F is the drive, d is the space moved, and θ is the angle between the drive and the displacement. Energy Energy is the speed at which work is finished. The components for energy is: “` P = W/t “` the place P is the ability, W is the work achieved, and t is the time. Effectivity Effectivity is the ratio of the helpful work achieved by a machine to the full work achieved. The components for effectivity is: “` η = W_useful/W_total “` the place η is the effectivity, W_useful is the helpful work achieved, and W_total is the full work achieved. Mechanical Benefit Mechanical benefit is the ratio of the output drive to the enter drive. The components for mechanical benefit is: “` MA = F_out/F_in “` the place MA is the mechanical benefit, F_out is the output drive, and F_in is the enter drive. Best Fuel Regulation The best fuel regulation is a mathematical equation that relates the stress, quantity, temperature, and variety of moles of a fuel. The components for the perfect fuel regulation is: “` PV = nRT “` the place P is the stress, V is the amount, n is the variety of moles, R is the perfect fuel fixed, and T is the temperature. Purposes of Fractions in Engineering Fractions are a elementary mathematical idea that discover widespread functions in varied engineering disciplines. Engineers make the most of fractions to symbolize ratios, mannequin bodily portions, and carry out calculations associated to design, evaluation, and optimization. 27. Mechanical Engineering In mechanical engineering, fractions play a vital position in: Gear Ratios: Gears are important parts in mechanical programs, and their efficiency depends upon the ratio of their enamel. Fractions are used to symbolize gear ratios, which decide the pace discount or enhance between gears. Stress Evaluation: Mechanical engineers analyze the stresses performing on buildings and parts to make sure their security and reliability. Fractions are used to symbolize stress concentrations, which point out areas of elevated stress that require reinforcement. Fluid Circulate: Fractions are used to characterize the move charge of fluids via pipes and different conduits. The Reynolds quantity, a dimensionless parameter used to foretell turbulent move, is expressed as a fraction. Materials Properties: The mechanical properties of supplies, resembling tensile power and yield power, are sometimes expressed as fractions to convey their relative power and ductility. Dimensional Tolerances: Fractions are used to specify dimensional tolerances in engineering drawings. These tolerances decide the appropriate vary of variation in dimensions, guaranteeing correct match and performance of parts. Conversion of Models: Mechanical engineers usually have to convert between completely different models of measurement. Fractions are used to facilitate these conversions, resembling changing toes to inches or kilograms to kilos. The next desk supplies particular examples of functions: Utility Fraction Illustration Gear Ratio 12/30 Stress Focus Issue 2.5 Reynolds Quantity ρVD/μ Tensile Power 20,000 psi Dimensional Tolerance ±0.005 in Purposes of Fractions in Laptop Science 1. Fractals Fractals are geometric patterns that repeat themselves at completely different scales. They’re usually used to create computer-generated artwork. Fractions are used to explain the scaling of fractals. For instance, the Koch snowflake is a fractal that’s generated by repeatedly dividing a triangle into smaller and smaller triangles. The ratio of the size of the facet of a smaller triangle to the size of the facet of the bigger triangle is a continuing fraction, often called the scaling issue. The scaling issue determines the general dimension of the snowflake. 2. Information Compression Information compression is the method of decreasing the dimensions of a file with out shedding any data. Fractions are utilized in some information compression algorithms, such because the Lempel-Ziv-Welch (LZW) algorithm. LZW works by changing repeated sequences of symbols with shorter codes. The codes are represented as fractions, the place the numerator is the variety of instances the image has been seen and the denominator is the full variety of symbols within the file. This permits for extra environment friendly storage and transmission of information. 3. Laptop Graphics Fractions are utilized in laptop graphics to symbolize the coordinates of factors in house. The x- and y-coordinates of a degree are sometimes represented as fractions of the width and top of the display screen, respectively. This permits for the exact positioning of objects in a 2D or 3D scene. Fractions are additionally used to symbolize colours in laptop graphics. The purple, inexperienced, and blue parts of a colour are sometimes represented as fractions of the utmost potential worth for every element. 4. Synthetic Intelligence Fractions are utilized in synthetic intelligence (AI) to symbolize chances. A chance is a worth between 0 and 1 that expresses the probability of an occasion occurring. Fractions are additionally utilized in AI to symbolize the weights of various options in a machine studying mannequin. The weights decide how a lot affect every characteristic has on the mannequin’s predictions. 5. Robotics Fractions are utilized in robotics to manage the motion of robots. The pace and course of a robotic’s motion are sometimes represented as fractions. For instance, a robotic may be commanded to maneuver ahead at a pace of 0.5 meters per second. Which means that the robotic will transfer ahead by 0.5 meters for each second that it’s working. 6. Laptop Networks Fractions are utilized in laptop networks to symbolize IP addresses. An IP tackle is a singular identifier for a tool on a community. IP addresses are sometimes represented as 4 octets, every of which is a fraction between 0 and 255. For instance, the IP tackle 192.168.1.1 represents the machine with the next octets: 192, 168, 1, and 1. 7. Net Growth Fractions are utilized in net growth to specify the sizes and positions of components on an online web page. The width and top of a component will be specified as fractions of the width and top of its mum or dad aspect. This permits for the creation of responsive net pages that routinely alter their structure to suit completely different display screen sizes. 8. Recreation Growth Fractions are utilized in sport growth to symbolize the well being, mana, and different attributes of characters and objects. Fractions are additionally used to symbolize the chances of various occasions occurring in a sport. For instance, a sport would possibly use a random quantity generator to find out the chance of a personality hitting an enemy with an assault. The chance could be represented as a fraction between 0 and 1. 9. Arithmetic Fractions are utilized in arithmetic to symbolize a variety of mathematical ideas, resembling ratios, proportions, and percentages. Fractions are additionally utilized in algebra, geometry, and calculus. For instance, the equation y = mx + b represents a straight line, the place m is the slope of the road and b is the y-intercept. The slope is represented as a fraction, the place the numerator is the change in y and the denominator is the change in x. 10. Physics Fractions are utilized in physics to symbolize a variety of bodily portions, resembling pace, acceleration, and drive. Fractions are additionally used within the equations of movement, which describe the movement of objects in house. For instance, the equation F = ma represents the second regulation of movement, the place F is the drive performing on an object, m is the mass of the article, and a is the acceleration of the article. The acceleration is represented as a fraction, the place the numerator is the change in velocity and the denominator is the change in time. 11. Chemistry Fractions are utilized in chemistry to symbolize the composition of chemical compounds. The chemical components of a compound signifies the ratio of the completely different components within the compound. For instance, the chemical components for water is H2O, which signifies that there are two atoms of hydrogen for each one atom of oxygen. The ratio of hydrogen to oxygen in water will be represented because the fraction 2/1. 12. Biology Fractions are utilized in biology to symbolize a variety of organic ideas, resembling inhabitants density, development charges, and genetic variety. Fractions are additionally used within the equations that describe the expansion and habits of organisms. For instance, the logistic development equation describes the expansion of a inhabitants in a restricted surroundings. The equation features a fraction that represents the carrying capability of the surroundings, which is the utmost variety of people that the surroundings can assist. 13. Drugs Fractions are utilized in medication to symbolize a variety of medical ideas, resembling dosages of medicines, blood stress, and physique mass index (BMI). Fractions are additionally used within the equations that describe the operate of the human physique. For instance, the Fick equation describes the connection between cardiac output, oxygen consumption, and arteriovenous oxygen distinction. The equation features a fraction that represents the arteriovenous oxygen distinction. 14. Economics Fractions are utilized in economics to symbolize a variety of financial ideas, resembling inflation charges, rates of interest, and unemployment charges. Fractions are additionally used within the equations that describe the habits of financial programs. For instance, the Keynesian multiplier describes the impact of presidency spending on mixture demand. The equation features a fraction that represents the marginal propensity to eat. 15. Psychology Fractions are utilized in psychology to symbolize a variety of psychological ideas, resembling intelligence quotients (IQs), character traits, and psychological well being issues. Fractions are additionally used within the equations that describe the habits of people and teams. For instance, the Fechner-Weber regulation describes the connection between the depth of a stimulus and the notion of the stimulus. The equation features a fraction that represents the Weber fraction. 16. Sociology Fractions are utilized in sociology to symbolize a variety of social ideas, resembling revenue inequality, social mobility, and crime charges. Fractions are additionally used within the equations that describe the habits of social programs. For instance, the Gini coefficient describes the inequality of revenue distribution in a society. The equation features a fraction that represents the cumulative distribution of revenue. 17. Anthropology Fractions are utilized in anthropology to symbolize a variety of anthropological ideas, resembling kinship relations, cultural variety, and ritual practices. Fractions are additionally used within the equations that describe the habits of human societies. For instance, the Lévi-Strauss mannequin of kinship describes the connection between marriage and descent. The mannequin features a fraction that represents the descent of a lineage. 18. Linguistics Fractions are utilized in linguistics to symbolize a variety of linguistic ideas, such because the frequency of phonemes, the distribution of phrases, Utilizing Fractions to Convert Measurements The TI-84 Plus calculator can be utilized to transform between completely different models of measurement, together with fractions. This may be useful when you might want to convert a measurement from one unit to a different, resembling from inches to toes or from gallons to liters. To transform a measurement utilizing a fraction, you need to use the next steps: 1. Enter the measurement you need to convert into the calculator. 2. Press the “MODE” button and choose the “Math” possibility. 3. Press the “FRAC” button to enter the fraction mode. 4. Enter the fraction that you just need to use to transform the measurement. 5. Press the “ENTER” button. 6. The calculator will show the transformed measurement. For instance, to transform 1/2 of a gallon to liters, you’ll enter the next steps into the calculator: 1. Enter “1/2”. 2. Press the “MODE” button and choose the “Math” possibility. 3. Press the “FRAC” button. 4. Enter “gal”. 5. Press the “ENTER” button. 6. The calculator will show “1.8927 liters”. Changing Fractions to Decimals If you might want to convert a fraction to a decimal, you need to use the next steps: 1. Enter the fraction into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Dec” possibility. 5. Press the “ENTER” button. For instance, to transform 1/2 to a decimal, you’ll enter the next steps into the calculator: 1. Enter “1/2”. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Dec” possibility. 5. Press the “ENTER” button. 6. The calculator will show “0.5”. Changing Decimals to Fractions If you might want to convert a decimal to a fraction, you need to use the next steps: 1. Enter the decimal into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Dec” possibility. 5. Press the “ENTER” button. For instance, to transform 0.5 to a fraction, you’ll enter the next steps into the calculator: 1. Enter “0.5”. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Dec” possibility. 5. Press the “ENTER” button. 6. The calculator will show “1/2”. Changing Blended Numbers to Fractions If you might want to convert a combined quantity to a fraction, you need to use the next steps: 1. Enter the combined quantity into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Combine” possibility. 5. Press the “ENTER” button. For instance, to transform 1 1/2 to a fraction, you’ll enter the next steps into the calculator: 1. Enter “1 1/2”. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Combine” possibility. 5. Press the “ENTER” button. 6. The calculator will show “3/2”. Changing Fractions to Blended Numbers If you might want to convert a fraction to a combined quantity, you need to use the next steps: 1. Enter the fraction into the calculator. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Combine” possibility. 5. Press the “ENTER” button. For instance, to transform 3/2 to a combined quantity, you’ll enter the next steps into the calculator: 1. Enter “3/2”. 2. Press the “MATH” button. 3. Choose the “Frac” possibility. 4. Choose the “Combine” possibility. 5. Press the “ENTER” button. 6. The calculator will show “1 1/2”. Utilizing Fractions to Resolve Ratio Issues Introduction Ratios are used to match two or extra values. They are often expressed as a fraction, decimal, or %. For instance, the ratio of boys to women in a classroom will be written as 3:4, 0.75, or 75%. Fractions are a standard technique to specific ratios, particularly when the values aren’t complete numbers. Utilizing the TI-84 Plus to Resolve Ratio Issues The TI-84 Plus can be utilized to resolve quite a lot of ratio issues. To enter a fraction, press the “2nd” key adopted by the “alpha” key. Then, use the arrow keys to navigate to the “frac” possibility. Enter the numerator and denominator of the fraction, separated by a “/”. For instance, to enter the fraction 3/4, press 2nd alpha, then use the arrow keys to navigate to “frac”. Then, enter 3 (numerator) and 4 (denominator), separated by a “/”. Fixing a Ratio Downside To unravel a ratio drawback utilizing the TI-84 Plus, comply with these steps: Enter the ratio as a fraction. Arrange an equation to symbolize the issue. Resolve the equation for the unknown worth. Instance Suppose you may have a recipe that calls for two cups of flour to three cups of sugar. You need to make a half batch of the recipe. How a lot flour and sugar do you want? Answer: Enter the ratio as a fraction: 2/3 Arrange an equation to symbolize the issue: 2/3 = x/y Resolve the equation for the unknown worth: x = 1 and y = 1.5 Due to this fact, you want 1 cup of flour and 1.5 cups of sugar to make a half batch of the recipe. Superior Ratio Issues The TI-84 Plus will also be used to resolve extra superior ratio issues. For instance, you need to use the calculator to: Discover the unit charge of a ratio Examine ratios Resolve proportions Unit Fee The unit charge of a ratio is the ratio of 1 unit of the primary amount to 1 unit of the second amount. To search out the unit charge of a ratio, divide the primary amount by the second amount. For instance, suppose you may have a ratio of 12 miles to three hours. The unit charge of this ratio is 12 miles / 3 hours = 4 miles per hour. Evaluating Ratios To check ratios, you need to use the next guidelines: Two ratios are equal if they’ve the identical worth. If the primary ratio is larger than the second ratio, then the primary amount is larger than the second amount. If the primary ratio is lower than the second ratio, then the primary amount is lower than the second amount. Proportions A proportion is an equation that states that two ratios are equal. Proportions can be utilized to resolve quite a lot of issues, resembling discovering lacking values or fixing phrase issues. To unravel a proportion, cross-multiply and clear up for the unknown worth. For instance, to resolve the proportion 2/3 = x/6, cross-multiply to get 2 * 6 = 3 * x. Then, clear up for x to get x = 4. Utilizing Fractions to Estimate Values The TI-84 Plus calculator can be utilized to estimate values of fractions. This may be useful for getting a fast approximation of a worth with out having to carry out an extended division calculation. To estimate a worth of a fraction, comply with these steps: Enter the fraction into the calculator. Press the “enter” key. The calculator will show the decimal worth of the fraction. For instance, to estimate the worth of 1/2, enter 1/2 into the calculator and press the “enter” key. The calculator will show the decimal worth 0.5. Utilizing Fractions to Estimate Values with a Bigger Quantity within the Denominator (instance: 40) When the denominator of a fraction is a big quantity, it may be tough to estimate the worth of the fraction. Nevertheless, there are a couple of strategies that can be utilized to get an excellent approximation. One methodology is to make use of the “fraction button” on the calculator. This button is positioned on the principle display screen of the calculator, and it seems like a fraction with a line via it. To make use of the fraction button, comply with these steps: Press the “fraction button”. Enter the numerator of the fraction. Press the “enter” key. Enter the denominator of the fraction. Press the “enter” key. The calculator will show the decimal worth of the fraction. For instance, to estimate the worth of 1/40, press the “fraction button”, enter 1, press the “enter” key, enter 40, and press the “enter” key. The calculator will show the decimal worth 0.025. One other methodology for estimating the worth of a fraction with a big denominator is to make use of the “desk” operate on the calculator. This operate can be utilized to create a desk of values for the fraction. To make use of the “desk” operate, comply with these steps: Press the “2nd” key after which the “desk” key. Enter the equation for the fraction. Press the “enter” key. Enter the beginning worth for the unbiased variable. Press the “enter” key. Enter the ending worth for the unbiased variable. Press the “enter” key. Enter the step worth for the unbiased variable. Press the “enter” key. The calculator will show a desk of values for the fraction. For instance, to create a desk of values for the fraction 1/40, enter 1/40 into the calculator, press the “enter” key, enter 0 into the calculator, press the “enter” key, enter 100 into the calculator, press the “enter” key, and enter 10 into the calculator. The calculator will show a desk of values for the fraction 1/40, as proven within the following desk: x y 0 0.025 10 0.25 20 0.5 30 0.75 40 1 As you may see from the desk, the worth of 1/40 is roughly 0.025. This can be a good approximation, regardless that the denominator of the fraction is comparatively massive. Utilizing Fractions to Characterize Likelihood Fractions can be utilized to symbolize chance. Likelihood is a measure of the probability that an occasion will happen. It’s expressed as a quantity between 0 and 1, the place 0 implies that the occasion is inconceivable and 1 implies that the occasion is for certain. For instance, the chance of rolling a 6 on a die is 1/6, as a result of there may be one consequence out of six potential outcomes that can end in a 6. Fractions will also be used to match chances. For instance, the chance of rolling a 6 on a die is larger than the chance of rolling a 1, as a result of there may be one consequence out of six potential outcomes that can end in a 6, however just one consequence out of six potential outcomes that can end in a 1. Utilizing Fractions to Resolve Likelihood Issues Fractions can be utilized to resolve chance issues. Listed here are some examples: What’s the chance of drawing a purple card from a deck of 52 playing cards? There are 26 purple playing cards in a deck of 52 playing cards. So the chance of drawing a purple card is 26/52 = 1/2. What’s the chance of rolling a 6 on a die after which rolling a 2? The chance of rolling a 6 on a die is 1/6. The chance of rolling a 2 on a die is 1/6. The chance of rolling a 6 after which rolling a 2 is (1/6) * (1/6) = 1/36. What’s the chance of getting heads on a coin toss after which tails on the second coin toss? The chance of getting heads on a coin toss is 1/2. The chance of getting tails on a coin toss is 1/2. The chance of getting heads after which tails is (1/2) * (1/2) = 1/4. Utilizing Fractions to Characterize Percentages Fractions can be utilized to symbolize percentages. A share is a method of expressing a quantity as a fraction of 100. For instance, 50% is similar as 50/100 = 1/2. Fractions will also be used to transform percentages to decimals. To transform a share to a decimal, divide the proportion by 100. For instance, 50% is similar as 50/100 = 0.5. Utilizing Fractions to Resolve Share Issues Fractions can be utilized to resolve share issues. Listed here are some examples: What’s 25% of 100? 25% is similar as 25/100 = 1/4. So 25% of 100 is (1/4) * 100 = 25. What’s the share of 20 that’s 5? To search out the proportion of 20 that’s 5, divide 5 by 20 after which multiply by 100. So the proportion of 20 that’s 5 is (5/20) * 100 = 25%. What’s 12% of fifty? 12% is similar as 0.12. So 12% of fifty is 0.12 * 50 = 6. Utilizing Fractions in Actual-World Conditions Fractions are utilized in quite a lot of real-world conditions. Listed here are some examples: Cooking: Fractions are used to measure components in recipes. Building: Fractions are used to measure distances and angles. Finance: Fractions are used to calculate rates of interest and percentages. Drugs: Fractions are used to measure dosages of treatment. Science: Fractions are used to measure portions resembling temperature and quantity. 41. Utilizing Fractions to Resolve Sensible Issues Along with the examples given above, fractions will also be used to resolve quite a lot of different sensible issues. Listed here are a couple of examples: Mixing paint: If you wish to combine two completely different colours of paint, you need to use fractions to find out how a lot of every colour to make use of. For instance, if you wish to combine 1/2 gallon of purple paint with 1/4 gallon of blue paint, you would wish to make use of 2/3 gallon of purple paint and 1/3 gallon of blue paint. Dividing a pizza: If you wish to divide a pizza evenly amongst a gaggle of individuals, you need to use fractions to find out how a lot of the pizza every particular person ought to get. For instance, if you wish to divide a pizza evenly amongst 4 folks, you would wish to chop the pizza into 4 equal slices. Calculating reductions: If you wish to calculate a reduction, you need to use fractions to find out how a lot of the unique worth you’ll pay. For instance, if you wish to calculate a ten% low cost, you would wish to multiply the unique worth by 0.9. Conclusion Fractions are a flexible mathematical device that can be utilized to resolve quite a lot of issues. By understanding easy methods to use fractions, you may make your life simpler and extra environment friendly. Utilizing Fractions to Calculate Quantity The TI-84 Plus calculator can be utilized to calculate the amount of quite a lot of objects, together with rectangular prisms, cylinders, cones, and spheres. Fractions can be utilized in any of those calculations. To make use of the calculator to calculate the amount of an object utilizing fractions, comply with these steps: 1. Enter the size of the article. For an oblong prism, enter the size, width, and top. For a cylinder, enter the radius and top. For a cone, enter the radius and top. For a sphere, enter the radius. 2. Enter the components for the amount of the article. The components for the amount of an oblong prism is V = lwh. The components for the amount of a cylinder is V = πr²h. The components for the amount of a cone is V = (1/3)πr²h. The components for the amount of a sphere is V = (4/3)πr³. 3. Substitute the variables within the components with the values you entered in step 1. For instance, in case you are calculating the amount of an oblong prism with a size of 5, a width of three, and a top of two, you’ll enter the next components into the calculator: “` V = 5 * 3 * 2 “` 4. Consider the expression. The calculator will show the amount of the article. For instance, if you happen to entered the components from step 3 into the calculator, the calculator would show the next consequence: “` V = 30 “` The quantity of the oblong prism is 30 cubic models. Listed here are some examples of easy methods to use fractions to calculate the amount of objects utilizing the TI-84 Plus calculator: Object Components Instance Outcome Rectangular prism V = lwh V = (1/2) * 3 * 4 V = 6 Cylinder V = πr²h V = π * (1/2)² * 3 V = (3π)/4 Cone V = (1/3)πr²h V = (1/3)π * (1/4)² * 5 V = (5π)/48 Sphere V = (4/3)πr³ V = (4/3)π * (2/3)³ V = (32π)/27 Utilizing Fractions to Calculate Weight Fractions are a standard technique to symbolize elements of a complete. They can be utilized to calculate weight, amongst different issues. To make use of fractions to calculate weight, you might want to know the next: The load of the entire object The fraction of the article that you just need to calculate the load of After getting this data, you need to use the next components to calculate the load of the fraction: “` Weight of fraction = Weight of complete object * Fraction “` For instance, in case you have a 10-pound bag of rice and also you need to calculate the load of half of the bag, you’ll use the next components: “` Weight of half bag = 10 kilos * 1/2 = 5 kilos “` It’s also possible to use fractions to match weights. For instance, in case you have a 5-pound bag of sugar and a 3-pound bag of flour, you need to use the next components to match their weights: “` Weight of sugar / Weight of flour = 5 kilos / 3 kilos = 1.67 “` Which means that the sugar is 1.67 instances heavier than the flour. 48. Instance: Calculating the Weight of a Fraction of a Watermelon Suppose you may have a watermelon that weighs 12 kilos. You need to calculate the load of half of the watermelon. You should utilize the next components: “` Weight of half watermelon = 12 kilos * 1/2 = 6 kilos “` Due to this fact, half of the watermelon weighs 6 kilos. 121: How To Use Fractions On Ti 84 Plus Fractions will be entered into the TI-84 Plus in quite a lot of methods. 1) utilizing the Fraction template (Math > Templates > Fraction), 2) by urgent the “ALPHA” key adopted by the “” key (which produces the fraction bar), or 3) by utilizing the “MATH” key adopted by the “NUM” key (which produces quite a lot of fraction codecs). As soon as a fraction has been entered, it may be utilized in calculations identical to every other quantity. Listed here are some examples of easy methods to enter fractions into the TI-84 Plus: To enter the fraction 1/2, press the “MATH” key adopted by the “NUM” key, then choose the “1/x” possibility. To enter the fraction 3/4, press the “ALPHA” key adopted by the “” key, then enter “3/4”. To enter the fraction 5/6, press the “Math” key adopted by the “Templates” key, then choose the “Fraction” template. Enter the numerator (5) and denominator (6) of the fraction. As soon as a fraction has been entered, it may be utilized in calculations identical to every other quantity. For instance, so as to add the fractions 1/2 and three/4, press the “1/2” key, then press the “+” key, then press the “3/4” key. The TI-84 Plus will return the reply, which is 5/4. To multiply the fractions 1/2 and three/4, press the “1/2” key, then press the “*” key, then press the “3/4” key. The TI-84 Plus will return the reply, which is 3/8. Fractions will also be transformed to decimals by urgent the “MATH” key adopted by the “NUM” key, then deciding on the “FracDec” possibility. Folks Additionally Ask About 121: How To Use Fractions On Ti 84 Plus How do you simplify fractions on a TI 84 Plus? To simplify a fraction on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “Simplify” possibility. The TI-84 Plus will simplify the fraction and return the reply. How do you exchange a fraction to a decimal on a TI 84 Plus? To transform a fraction to a decimal on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracDec” possibility. The TI-84 Plus will convert the fraction to a decimal and return the reply. How do you add fractions on a TI 84 Plus? So as to add fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracAdd” possibility. The TI-84 Plus will add the fractions and return the reply. How do you subtract fractions on a TI 84 Plus? To subtract fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracSub” possibility. The TI-84 Plus will subtract the fractions and return the reply. How do you multiply fractions on a TI 84 Plus? To multiply fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracMult” possibility. The TI-84 Plus will multiply the fractions and return the reply. How do you divide fractions on a TI 84 Plus? To divide fractions on a TI-84 Plus, press the “MATH” key adopted by the “NUM” key, then choose the “FracDiv” possibility. The TI-84 Plus will divide the fractions and return the reply.