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So, you have a math problem where you’re tasked with multiplying fractions by whole numbers. Maybe the whole numbers are in a mixed fraction or by themselves. Either way, the task isn’t as difficult as you may think! In this article, we’ll walk you through the process of multiplying fractions with whole numbers. Plus, we’ve even provided practice problems and examples to help you understand the process better.
How do you multiply a fraction by a whole number?
- Write the whole number as a fraction with the whole number on top and 1 on the bottom.
- Multiply the top numbers (numerators) of the fractions
- Multiply the bottom numbers (denominators) of the fractions.
- Simplify your answer if you can.
Steps
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Rewrite the whole number as a fraction . Associate professor of mathematics Mario Banuelos, PhD explains, “To multiply fractions with whole numbers, simply convert the whole number to a fraction by dividing by 1.” [1] X 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 to make an improper fraction. [2] X Research source- For example, if you have 5 x 8/10, put the 5 over 1 to make the equation 5/1 x 8/10.
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Multiply the numerators of the fractions. The next step to multiplying fractions by whole numbers is to “multiply across,” according to Banuelos. [3] X Expert Source Mario Banuelos, PhD
Associate Professor of Mathematics Expert Interview. 11 December 2022. Multiply the numerators (or top numbers) together. This will be the numerator of your result. [4] X Research source- In the example, 5/1 x 8/10, multiply 5 by 8 to get 40. 40 is the numerator.
- The numerator is the number above the fraction line.
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Multiply the denominators of the two fractions. Multiply the numbers below the fraction lines to get your denominator. [5] X 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.
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Reduce the answer if possible. The majority of the time, your answer will be an improper fraction (a fraction where the numerator is greater than or equal to the denominator). If your answer is an improper fraction, simplify it to the lowest terms. Do this by dividing the numerator by the denominator to get a simplified result. [6] X Research source
- For example, to reduce 40/10, divide 40 by 10 to get 4 as your new answer.
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Convert the mixed fractions to improper fractions . To do this, first multiply the denominator (the bottom number) of the first fraction by the whole number. Then, add the number you get to the denominator. Place the result over the line and leave the denominator as is. Repeat with the second mixed fraction. [7] X Research source
- For example, say you start with 1 1/2 x 4 4/7.
- 1 1/2 becomes 3/2 because 1 x 2 + 1 = 3.
- 4 4/7 becomes 32/7 because 4 x 7 + 4 = 32.
- Your equation is now 3/2 x 32/7.
- An improper fraction is a fraction where the numerator is greater than or equal to the denominator. [8] X Research source
- For example, say you start with 1 1/2 x 4 4/7.
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Multiply the numerators of the improper fractions. Now that you have two improper fractions and no whole numbers in the equation, multiply the numerators (top numbers) together. Write the result and place a line below it. [9] X Research source
- For example, with 3/2 x 32/7, multiply 3 by 32 to get 96. 96 is the numerator.
- The numerator is always the top number in a fraction.
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Multiply the denominators of the improper fractions. Multiply the bottom numbers and write the result under your numerator. [10] X Research source
- For example, with 3/2 x 32/7, multiply the 2 by 7 to get 14.
- The denominator is always the bottom number in a fraction. Your fraction is now 96/14.
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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 can go into the numerator. Then, put the remainder over the denominator to create a mixed fraction . [11] X Research source
- For example, with our improper fraction 96/14:
- 14 can go into 96 six times.
- 14 x 6 = 84
- 96 - 84 = 12 (which is our remainder)
- Therefore, the answer is 6 12/14.
- For example, with our improper fraction 96/14:
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Simplify the fraction further if possible. Even when you turn the answer into a mixed fraction, the answer will probably be able to be simplified further. Look at the fraction and see if it can be reduced any further. [12] X Research source
- For example, 6 12/14 can be simplified to 6 6/7 because both the numerator and denominator can be divided by 2.
- When simplifying a mixed fraction, keep the whole number the same.
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Practice Problems
Community Q&A
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QuestionWhat if the question has two fractions, like 1/4 x 13 1/2?DonaganTop AnswererChange 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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QuestionPlease give an example of multiplying fractions and whole numbers.Community AnswerIf 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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QuestionHow do I work 1/5×7?SnallisonCommunity AnswerFirst, 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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Tips
- 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.Thanks
- Still unsure if your answer is correct? Check your work with an online fraction calculator like Calculator Soup .Thanks
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References
- ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2022.
- ↑ https://math.libretexts.org/Courses/Fullerton_College/Math_100:_Liberal_Arts_Math_(Claassen_and_Ikeda)/10:_Appendix/10.02:_Fractions_and_Mixed_Numbers/10.2.02:_Multiplying_and_Dividing_Fractions_and_Mixed_Numbers/10.2.2.01:_Multiplying_Fractions_and_Mixed_Numbers
- ↑ Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2022.
- ↑ https://www.cuemath.com/numbers/multiplying-fractions-with-whole-numbers/
- ↑ https://www.cuemath.com/numbers/multiplying-fractions-with-whole-numbers/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/7.1/primary/lesson/multiplication-of-fractions-and-whole-numbers-msm6/
- ↑ https://www.mathsisfun.com/mixed-fractions-multiply.html
- ↑ https://www.cuemath.com/numbers/improper-fractions/
- ↑ https://www.mathsisfun.com/mixed-fractions-multiply.html
About This Article
Article Summary
X
To multiply a fraction by a whole number, first rewrite the whole number as a fraction by putting it over a 1. For example, let’s say you’re trying to solve 5 x 8/10. You would start by rewriting 5 as a fraction. Now the equation looks like 5/1 x 8/10. Next you need to multiply the numerators, or top numbers, of the fractions together. In our example, 5 and 8 are the numerators, so you would multiply 5 by 8 and get 40. Now do the same thing with the denominators, or bottom numbers, of the fractions. One and 10 are the denominators, so you would multiply 1 by 10 and get 10. The new fraction is 40/10. If you can’t simplify the new fraction, you’re done and that’s your answer. If you can, simplify the fraction to the lowest terms. In our example we ended up with 40/10, which can be simplified by dividing the numerator and denominator by 10, which gives you 4/1. Therefore, 5 x 8/10 = 4/1, or 4. To learn how to multiply a normal fraction with a whole number, scroll down!
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