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How to Divide Fractions by a Whole Number Download ArticleExplore this Article Steps Steps Other Sections Questions & Answers Tips and Warnings Related Articles References Article Summary Co-authored by David Jia
Last Updated: November 15, 2024 Fact Checked
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This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 968,531 times.
Dividing fractions by a whole number isn't as hard as it looks. To divide a fraction by a whole number, all you have to do is to convert the whole number into a fraction, find the reciprocal of that fraction, and multiply the result by the first fraction. If you want to know how to do it, just follow these steps:
Dividing Fractions with Whole Numbers
Change the whole number into a fraction by placing it over the number 1. Switch the numerator and denominator of the whole number and change the division sign into a multiplication sign. Multiply the numerators, then multiply the denominators. Simplify the fraction into the lowest common denominator.
Practice Problems
Divide Fractions by a Whole Number Practice ProblemsDivide Fractions by a Whole Number Practice Problems ANSWER KEY
Steps
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1 Write the problem. The first step to dividing a fraction by a whole number is to simply write out the fraction followed by the division sign and the whole number you need to divide it by. Let's say we're working with the following problem: 2/3 ÷ 4.[1]XResearch source
2 Change the whole number into a fraction. To change a whole number into a fraction, all you have to do is place the number over the number 1. The whole number becomes the numerator and 1 becomes the denominator of the fraction. Saying 4/1 is really the same as saying 4, since you're just showing that the number includes "1" 4 times. The problem should read 2/3 ÷ 4/1.[2]XResearch source Advertisement
3 Dividing a fraction by another fraction is the same as multiplying that fraction by the reciprocal of the other fraction.[3]XResearch source [4]X Expert Source David JiaAcademic TutorExpert Interview
4 Write the reciprocal of the whole number. To find the reciprocal of a number, simply switch the numerator and the denominator of the number.[5]X Expert Source David JiaAcademic TutorExpert Interview Therefore, to find the reciprocal of 4/1, simply switch the numerator and denominator so that the number becomes 1/4.[6]XResearch source
5 Change the division sign into a multiplication sign. The problem should read 2/3 x 1/4.[7]XResearch source
6 Multiply the numerators and denominators of the fractions. Therefore, the next step is to multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final answer.[8]XResearch source
To multiply the numerators, just multiply 2 x 1 to get 2.
To multiply the denominators, just multiply 3 x 4 to get 12.
2/3 x 1/4 = 2/12
7 Simplify the fraction. To simply the fraction, you need to find the lowest common denominator, which means that you should divide both the numerator and denominator by any number that divides evenly into both numbers. Since 2 is the numerator, you should see if 2 divides evenly into 12 -- it does because 12 is even. Then, divide both the numerator and denominator by 2 to get the new numerator and denominator to get a simplified answer.[9]XResearch source
2 ÷ 2 = 1
12 ÷ 2 = 6
The fraction 2/12 can be simplified to 1/6. This is your final answer.
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
To simplify fractions, you can divide both the numerator and denominator by a common factor. This creates a new, easier-to-use fraction with smaller components, but it represents the same value. For instance, if you divide both the numerator and denominator of 6/12 by 2, you get 3/6, which is equal to 1/2.
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Question One fourth is 0.25. Dividing 0.25 by 3, we get 0.083. What is the fraction? Donagan Top Answerer If you want the answer in the form of a fraction, don't convert to a decimal in the first place. Just divide ¼ by 3. That's 1/12. 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 53 Helpful 87
Question What is 2 divided by 2/3? Donagan Top Answerer Invert 2/3, then multiply it by 2. 2/3 inverts to 3/2. 3/2 multiplied by 2 is 6/2, or 3. 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 53 Helpful 71
Question What is 15 divided by 1 4/5 in fraction form? Donagan Top Answerer Convert the mixed number to an improper fraction. Invert it and multiply by the whole number. Reduce the resulting fraction if possible. 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 42 Helpful 68
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Tips
Here's a mnemonic, an easy way to remember how to do all of this. Remember the following: "Dividing fractions is easy as pie, flip the second number and multiply!" Thanks Helpful 2 Not Helpful 1
Another Variation of the above is KCF/KFC. Keep the first number. Change to multiplication. Flip the last number. Or F before C. Thanks Helpful 1 Not Helpful 0
If you cross-cancel before you multiply, you probably won't need to reduce to lowest terms because its already on its lowest term as you can see. In our example, before we multiply 2/3 × 1/4, we might notice that the first numerator (2) and the second denominator (4) have a common factor of 2, which we can cancel in advance. This changes the problem to 1/3 × 1/2, giving us 1/6 immediately and saving us the work of reducing the fraction at the end. Thanks Helpful 0 Not Helpful 0
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Warnings
Only take the reciprocal of the second fraction, the one you're dividing by. Don't change the first one, the one you're dividing into. In our example, we converted the 4/1 to 1/4, but we left the 2/3 as 2/3 (we didn't change it to 3/2). Thanks Helpful 3 Not Helpful 1
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 968,531 times. 70 votes - 77% Co-authors: 113Updated: November 15, 2024 Views: 968,531 Categories: Multiplication and Division | FractionsArticle SummaryX
To divide a fraction by a whole number, start by writing the whole number over 1 so it looks like a fraction. Then, find the reciprocal of the whole number by switching the numerator and denominator. Your reciprocal should look like 1 over the whole number. When you “divide” fractions by whole numbers, you actually multiply the fraction by the reciprocal of the whole number. To do so, multiply the numerators and denominators of the two fractions. Finally, simplify the result as much as you can. If you want to learn more, like how to simplify your fraction when you're finished, keep reading the article!Did this summary help you?YesNo
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Download Article Explore this Article Steps Steps Other Sections Questions & Answers Tips and Warnings Related Articles References Article Summary Co-authored by David Jia 
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Co-authored by: David Jia Math Tutor This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 968,531 times. 70 votes - 77% Co-authors: 113 Updated: November 15, 2024 Views: 968,531 Categories: Multiplication and Division | Fractions Article SummaryX
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Divide Fractions by a Whole Number Practice Problems 
Divide Fractions by a Whole Number Practice Problems ANSWER KEY 
1 Write the problem. The first step to dividing a fraction by a whole number is to simply write out the fraction followed by the division sign and the whole number you need to divide it by. Let's say we're working with the following problem: 2/3 ÷ 4.[1] 
2 Change the whole number into a fraction. To change a whole number into a fraction, all you have to do is place the number over the number 1. The whole number becomes the numerator and 1 becomes the denominator of the fraction. Saying 4/1 is really the same as saying 4, since you're just showing that the number includes "1" 4 times. The problem should read 2/3 ÷ 4/1.[2] Advertisement 
3 Dividing a fraction by another fraction is the same as multiplying that fraction by the reciprocal of the other fraction.[3] [4] 
4 Write the reciprocal of the whole number. To find the reciprocal of a number, simply switch the numerator and the denominator of the number.[5] Therefore, to find the reciprocal of 4/1, simply switch the numerator and denominator so that the number becomes 1/4.[6] 
5 Change the division sign into a multiplication sign. The problem should read 2/3 x 1/4.[7] 
6 Multiply the numerators and denominators of the fractions. Therefore, the next step is to multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final answer.[8] 
7 Simplify the fraction. To simply the fraction, you need to find the lowest common denominator, which means that you should divide both the numerator and denominator by any number that divides evenly into both numbers. Since 2 is the numerator, you should see if 2 divides evenly into 12 -- it does because 12 is even. Then, divide both the numerator and denominator by 2 to get the new numerator and denominator to get a simplified answer.[9] 
Donagan Top Answerer If you want the answer in the form of a fraction, don't convert to a decimal in the first place. Just divide ¼ by 3. That's 1/12. 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 53 Helpful 87