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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:
Practice Problems
Steps
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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]
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
Write the reciprocal of the whole number. To find the reciprocal of a number, simply switch the numerator and the denominator of the number. Therefore, to find the reciprocal of 4/1, simply switch the numerator and denominator so that the number becomes 1/4.[4]
Change the division sign into a multiplication sign. The problem should read 2/3 x 1/4.[5]
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.[6]- 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
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.[7]- 2 ÷ 2 = 1
- 12 ÷ 2 = 6
- The fraction 2/12 can be simplified to 1/6. This is your final answer.
EXPERT TIPJoseph 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.Math Teacher
Joseph Meyer
Math TeacherTo 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.
Community Q&A
- QuestionOne fourth is 0.25. Dividing 0.25 by 3, we get 0.083. What is the fraction?
DonaganTop AnswererIf 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. - QuestionWhat is 2 divided by 2/3?DonaganTop AnswererInvert 2/3, then multiply it by 2. 2/3 inverts to 3/2. 3/2 multiplied by 2 is 6/2, or 3.
- QuestionWhat is 15 divided by 1 4/5 in fraction form?DonaganTop AnswererConvert the mixed number to an improper fraction. Invert it and multiply by the whole number. Reduce the resulting fraction if possible.
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
- Another Variation of the above is KCF/KFC. Keep the first number. Change to multiplication. Flip the last number. Or F before C.Thanks
- 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
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
References
- ↑ http://www.mathsisfun.com/numbers/fractions-division-whole-numbers.html
- ↑ https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/x0267d782:dividing-fractions-and-whole-numbers/v/visually-dividing-a-fraction-by-a-whole-number
- ↑ https://www.ck12.org/c/arithmetic/divide-fractions-and-whole-numbers/lesson/Division-of-Fractions-by-Whole-Numbers-MSM6/
- ↑ https://www.cuemath.com/numbers/dividing-fractions-with-whole-numbers/
- ↑ https://www.cuemath.com/numbers/dividing-fractions-with-whole-numbers/
- ↑ https://www.mathsisfun.com/numbers/fractions-division-whole-numbers.html
- ↑ https://www.mathsisfun.com/simplifying-fractions.html
About This Article
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!
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