How to Multiply Fractions With Whole Numbers

Co-authored by Mario Banuelos, PhD and Jessica Gibson

Last Updated: September 19, 2024 Fact Checked

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It's easy to multiply fractions by mixed fractions or whole numbers. Start by turning your mixed fractions or whole numbers into improper fractions. Then multiply the numerators of both improper fractions. Multiply the denominators and simplify your result.

Practice Problems

Multiply Fractions with Whole Numbers Practice Problems

ANSWER KEY - Multiply Fractions with Whole Numbers Practice Problems

Method 1

Method 1 of 2:

Multiplying Mixed Fractions by Mixed Fractions

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1
Convert the mixed fractions to improper fractions. To change 1 of the mixed fractions, multiply the denominator by the whole number. Then add the numerator. Place the result over the line and leave the denominator as-is. Repeat this for the other mixed fraction.^{[1]
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- For example, if you start with 1 1/2 x 4 4/7, change them to improper fractions. 1 1/2 will become 3/2 and 4 4/7 will become 32/7. Your equation will now by 3/2 x 32/7.
$Step 2 Multiply the numerators of the improper fractions.$

2
Multiply the numerators of the improper fractions. Now that you have 2 improper fractions and no whole numbers in the equation, multiply the numerators together. Write the result and place a line below it.^{[2]
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- The numerator is always the top number in a fraction.
- For example, with 3/2 x 32/7, multiply 3 by 32 to get 96.
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$Step 3 Multiply the denominators of the improper fractions.$

3
Multiply the denominators of the improper fractions. Multiply the numbers below the line and write the result under your numerator.^{[3]
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- For example, with 3/2 x 32/7, multiply the 2 by 7 to get 14.
$Step 4 Turn the answer into a mixed fraction if possible.$

4
Turn the answer into a mixed fraction if possible. If the numerator of your result is larger than the denominator, see how many times the denominator will go into the numerator. Then leave put the remainder over the denominator to give you a mixed fraction.^{[4]
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- For example, if you got 96/14, see how many times 14 will go into 96. You'll get 6 with 12 left over. Place 12 over the denominator (14).
- Most instructors will want you to put the answer in the same form as the question. So if you started with mixed fractions, convert your answer to a mixed fraction.
5
Simplify further if possible. You'll probably end up with a whole number and a fraction. Look at the fraction and see if you can simplify it. For example, if you have 6 12/14, reduce 12/14 by 2 to get 6/7.^{[5]
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- In this example, your final answer will be 6 6/7.

Method 2

Method 2 of 2:

Multiplying Fractions by Whole Numbers

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1
Rewrite the whole number as a fraction.^{[6]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2022.} To rewrite a whole number as a fraction, simply place the whole number over 1. This will make an improper fraction.^{[7]
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Research source}
- For example, if you have 5 x 8/10, put the 5 over 1. You should now have 5/1 x 8/10.
$Step 2 Multiply the numerators of the two fractions.$

2
Multiply the numerators of the two fractions.^{[8]
X
Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2022.} Remember that the numerators are the numbers above the lines. Write the result and place a line below it.^{[9]
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Research source}
- In the example, 5/1 x 8/10, multiply 5 by 8 to get 40.
$Step 3 Multiply the denominators of the two fractions.$

3
Multiply the denominators of the two fractions.^{[10]
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Expert Source

Mario Banuelos, PhD
Associate Professor of Mathematics

Expert Interview. 11 December 2022.} Now you can multiply the numbers below the lines to get your denominator. You should now have an answer to your equation that's in fraction form.^{[11]
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Research source}
- For example, if you're multiplying 5/1 x 8/10, multiply 1 by 10 to get 10. Place this below the line to get an answer of 40/10.
4
Reduce the answer if possible. Because your answer will probably be an improper fraction, simplify the answer to its lowest terms. Divide the numerator by the denominator to get a simplified result.^{[12]
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- To reduce 40/10, divide 40 by 10 to get 4 as your new answer.
- In many cases, you'll get a mixed number since the answer will have a remainder.

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Question

What if the question has two fractions, like 1/4 x 13 1/2?

Donagan

Top Answerer

Change the mixed number to an improper fraction, then multiply numerator by numerator and denominator by denominator. Simplify the answer if possible, and change it back to a mixed number if you like.

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Please give an example of multiplying fractions and whole numbers.

Community Answer

If you have a question of say, 4 x 2/3, take the 4 first, and put it out of 1, making it 4/1. The reason is that it's 4 wholes. To check, you can simplify 4/1, which will be 4, so it's obviously right.Then, taking 4/1 x 2/3, multiply the numerators first. The numerators, which are 4 and 2, will be multiplied to make 8. Question so far: 4/1 x 2/3= 8/? To find the denominator of the answer, take the denominators of the question, 1 and 3, and multiply those together. 1 multiplied by 3 will be 3. Question Answered: 4/1 x 2/3= 8/3. So, your answer is 8/3, and there you have it.

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How do I work 1/5×7?

Snallison

Community Answer

First, you make 7 into a fraction by putting it over 1, to create 7/1. Then you multiply across the top and across the bottom, which gives you 7/5. Because this is improper, you have to make this into a mixed number. To fix this, you have to divide 7 by 5. The answer is 1 with a remainder of 2. 1 is the whole number and 2 goes over the original denominator, 5. The final answer is 1 2/5.

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Remember that if you multiply a negative value by a positive value, the answer will be negative. However, if you have a negative value and a negative value, the negatives will cancel each other, giving you a positive result.

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