How Do You Divide a Whole Number by a Fraction? A Step-by-Step Guide

Download Article

A study guide with visual & video steps to divide numbers by fractions

Co-authored by Sophie Burkholder, BA Reviewed by Grace Imson, MA

Last Updated: March 31, 2025 Fact Checked

Download Article

Multiplying Reciprocals Method

|

Diagram Method

|

Sample Problems & Solutions

|

Video

|

Q&A

When dividing a whole number by a fraction, you are finding how many groups of the fraction you can fit in the whole. The standard way of dividing a whole number by a fraction is to multiply the whole number by the reciprocal of the fraction. You can also draw a diagram to help you visualize the process. We’ll walk you through both methods below, along with some example math problems with step-by-step solutions.

Dividing Whole Numbers by Fractions

Flip the fraction so that the numerator and denominator are in opposite spots. Then, convert your whole number to a fraction by placing 1 as its denominator. Multiply the two fractions together by multiplying their numerators together, then their denominators together. Simplify your answer as needed.

Section 1 of 3:

Dividing a Number by a Fraction: Reciprocal Method

Download Article

1
Give the whole number the denominator “1” to make it a fraction. To turn the whole number into a fraction, use the number as the numerator (the number on top of the fraction). Then, use the number 1 as the denominator (the number on the bottom of the fraction). ^{[1]
X
Research source}
- For example, if you are calculating $7\div {\frac {3}{4}}$ , you would first change $7$ to ${\frac {7}{1}}$ .
2
Flip the original fraction to find its reciprocal. Take the divisor (the starting fraction that you’re trying to divide by— not the fraction you made out of the whole number). Reverse the numerator and denominator to find the fraction’s inverse, also known as the reciprocal. ^{[2]
X
Research source}
- For example, the inverse of ${\frac {3}{4}}$ is ${\frac {4}{3}}$ .
Advertisement
3
Multiply the numerators together, then multiply the denominators together. To multiply fractions , first multiply the numerators together. Then, multiply the denominators together. The product of the two fractions equals the quotient of your original division problem. In other words, the result you get from this multiplication step is the answer to your division problem. ^{[3]
X
Research source}
- For example, ${\frac {7}{1}}\times {\frac {4}{3}}={\frac {28}{3}}$
4
Simplify the fraction, if necessary. Usually, your teacher will require you to reduce proper fractions to their lowest terms. If you have an improper fraction (a fraction with a larger numerator than denominator), your teacher may require you to change it to a mixed number . ^{[4]
X
Research source}
- To reduce a proper fraction, find the greatest common factor between the numerator and the denominator—aka the highest number that divides evenly into both numbers. Then, divide both the numerator and denominator by the GCF to get the new numerator and the new denominator, respectively, says academic tutor David Jia.
- For example, ${\frac {28}{3}}$ simplifies to the mixed number $9{\frac {1}{3}}$ .
EXPERT TIP

Joseph Meyer
Math Teacher
Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

Joseph Meyer
Math Teacher

Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.

Section 2 of 3:

Dividing a Number by a Fraction: Diagram Method

Download Article

1
Draw enough large shapes to match the count of the whole number. If your whole number is 5, for instance, draw 5 large-ish shapes. Each shape should be capable of being divided into equal groups, such as a square or circle. Draw the shapes large enough that you can divide them into smaller pieces. ^{[5]
X
Research source}
- For example, if you are calculating $5\div {\frac {3}{4}}$ , you would draw 5 circles.
2
Divide each whole shape according to the fraction’s denominator. The denominator of a fraction tells you how many pieces a whole is divided into. Divide each whole shape into its fractional parts. ^{[6]
X
Research source}
- For example, if you are dividing by ${\frac {3}{4}}$ , the 4 in the denominator tells you to divide each whole shape into fourths, giving you 20 small sections overall.
3
Shade in the same number of sections per shape as the numerator. Since you are dividing the whole number by the fraction, you are looking to see how many groups of the fraction are in the whole number. ^{[7]
X
Research source} So, first, you need to create your groups. It might be helpful to shade each group a different color, since some groups will have pieces in two different wholes. Leave any leftover pieces unshaded.
- For example, if you are dividing 5 by ${\frac {3}{4}}$ , you would color 3 quarters a different color for each group. Note that many groups will contain 2 quarters in one whole, and 1 quarter in another whole.
4
Count the number of whole groups that have been shaded in. This will give you the whole number of your answer. ^{[8]
X
Research source}
- For example, you should have created 6 groups of ${\frac {3}{4}}$ among your 5 circles.
5
Compare the number of pieces you have leftover to a complete group. The fraction of a group that you have left over will indicate the fraction of your answer. Make sure you do not compare the number of pieces you have to a whole shape, as this will give you the wrong fraction. ^{[9]
X
Research source}
- For example, after dividing the 5 shapes into groups of ${\frac {3}{4}}$ , you have 2 quarters, or ${\frac {2}{4}}$ left. Since a whole group is 3 pieces, and you have 2 pieces, your fraction is ${\frac {2}{3}}$ .
6
Combine your whole and fractional numbers to write your answer. Combine your whole number of groups with your fractional number of groups to find the quotient of your original division problem. ^{[10]
X
Research source}
- For example, $5\div {\frac {3}{4}}=6{\frac {2}{3}}$ .

Section 3 of 3:

Sample Problems & Solutions

Download Article

1
Sample Problem #1 How many times does ${\frac {1}{2}}$ go into $8$ ?
- Solution:
  - Since the problem is asking how many groups of ${\frac {1}{2}}$ are in 8, the problem is one of division.
  - Turn 8 into a fraction by placing it over 1: $8={\frac {8}{1}}$ .
  - Find the reciprocal of the fraction by reversing the numerator and denominator: ${\frac {1}{2}}$ becomes ${\frac {2}{1}}$ .
  - Multiply the two fractions together: ${\frac {8}{1}}\times {\frac {2}{1}}={\frac {16}{1}}$ .
  - Simplify, if necessary: ${\frac {16}{1}}=16$ .
2
Sample Problem #2 Solve $16\div {\frac {5}{8}}$ .
- Solution:
  - Convert 16 into a fraction by placing it over 1: $16={\frac {16}{1}}$ .
  - Take the fraction’s reciprocal by reversing the numerator and denominator: ${\frac {5}{8}}$ becomes ${\frac {8}{5}}$ .
  - Multiply the two fractions together: ${\frac {16}{1}}\times {\frac {8}{5}}={\frac {128}{5}}$ .
  - Simplify, if necessary: ${\frac {128}{5}}=25{\frac {3}{5}}$ .
3
Sample Problem #3 Rufus has 9 cans of food. She eats ${\frac {2}{3}}$ of a can every day. How many days will her food last?
- Solution:
  - Draw 9 circles representing the 9 cans.
  - Since she eats ${\frac {2}{3}}$ at a time, divide each circle into thirds.
  - Color groups of ${\frac {2}{3}}$ .
  - Count the number of complete groups. There should be 13.
  - Interpret the leftover pieces. There is 1 piece leftover, which is ${\frac {1}{3}}$ . Since a whole group is ${\frac {2}{3}}$ , you have half a group left over. So, your fraction is ${\frac {1}{2}}$ .
  - Combine the number of whole groups and fractional groups to find your final answer: $9\div {\frac {2}{3}}=13{\frac {1}{2}}$ .

Video

Community Q&A

Search

Add New Question

Question

What is 12 3/7 divided by 9?

Donagan

Top Answerer

First convert 12 3/7 to the improper fraction 87/7. Then divide by 9. The easiest way to do that is to multiply the denominator by 9: 7 x 9 = 63. So 87/7 ÷ 9 = 87/63, which reduces to 29/21. If you want the answer in mixed-number form, it's 1 8/21.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 17 Helpful 23
Question

How do I will simplify 24/1?

Donagan

Top Answerer

24/1 = 24.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 22 Helpful 20
Question

How do I divide 100,000 to 8 shares and 1/2 share?

Donagan

Top Answerer

Divide 100,000 by 8.5.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 21 Helpful 19

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Tips

Submit a Tip

All tip submissions are carefully reviewed before being published

Name

Please provide your name and last initial

Submit

Thanks for submitting a tip for review!

You Might Also Like

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

Log in

How Do You Divide a Whole Number by a Fraction? A Step-by-Step Guide

Dividing Whole Numbers by Fractions

Steps

Dividing a Number by a Fraction: Reciprocal Method

Dividing a Number by a Fraction: Diagram Method

Sample Problems & Solutions

Video

Community Q&A

Tips

You Might Also Like

References

About This Article

Reader Success Stories

Did this article help you?

Quizzes

You Might Also Like

Featured Articles

Trending Articles

Featured Articles

Featured Articles

Watch Articles

Trending Articles

Quizzes

Explore Categories