This article was co-authored by Mario Banuelos, PhD. Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.
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A mixed number is a whole number next to a fraction, such as 3 ½. Multiplying two mixed numbers can be tricky, because you have to convert them to improper fractions first. If you want to know how to multiply mixed numbers, you can learn how to do it just by following a few easy steps.
Steps
Practice Problems
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1Consider multiplying 41/2 with 62/5
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2Convert your first mixed number to an improper fraction. An improper fraction is a number that has a numerator that is larger than its denominator.[1] You can convert a mixed number to an improper fraction in just these easy steps:
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Multiply the whole number by the denominator of the fraction.[2]
If you are converting the number 41/2 to an improper fraction, you would first multiply the whole number 4 by the denominator of the fraction which is 2. So, 4 x 2 = 8 -
Add this number to the numerator of the fraction.
So adding 8 to the numerator 1, we get 8 + 1 = 9. -
Place this new number over the original denominator of the fraction.[3]
The new number is 9, so you can place it over 2, the original denominator.
The mixed number 41/2 converts to the improper fraction 9/2.
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Multiply the whole number by the denominator of the fraction.[2]
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3Convert your second mixed number to an improper fraction.
Follow exactly the same steps as described above:[4]-
Multiply the whole number by the denominator of the fraction.
If you are converting the number 62/5 to an improper fraction, you would first multiply the whole number 6 by the denominator of the fraction which is 5. So, 6 x 5 = 30 -
Add this number to the numerator of the fraction.
So adding 30 to the numerator 2, we get 30 + 2 = 32. -
Place this new number over the original denominator of the fraction.
The new number is 32, so you can place it over 5, the original denominator.
The mixed number 62/5 converts to the improper fraction 32/5.
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Multiply the whole number by the denominator of the fraction.
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4Multiply the two improper fractions. Once you've converted each of your mixed numbers to improper fractions, you can multiply them. To multiply the numbers, just multiply their numerators and multiply their denominators.[5]
- To multiply 9/2 and 32/5, you should multiply the numerators, 9 and 32. So 9 x 32 = 288.
- Next, multiply the denominators, 2 and 5, to get 10.
- Place the new numerator over the new denominator to get 288/10.
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5Reduce your answer to the lowest terms. To reduce your fraction to the lowest terms, find the Greatest Common Factor (GCF), which is the biggest number that is divisible by both the numerator and the denominator. Then divide the numerator and denominator by this number.[6]
- 2 is the greatest common factor of both 288 and 10. Divide 288 by 2 to get 144, and divide 10 by 2 to get 5.
288/10 is reduced to 144/5.
- 2 is the greatest common factor of both 288 and 10. Divide 288 by 2 to get 144, and divide 10 by 2 to get 5.
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6Convert your answer to a mixed number. Since the question is in mixed number form, the answer should be in mixed number form as well. To convert it to the mixed number, you have to work backwards to get your answer. Here's how you do it:[7]
- First, divide the top number by the bottom number.
Do long division to divide 5 into 144. 5 goes 28 times into 144. This means that the quotient is 28. The remainder, or the number that is left over, is 4. - Make your quotient the new whole number. Take your remainder and place it over the original denominator to finish converting the improper fraction into a mixed number.
The quotient is 28, the remainder is 4, and the original denominator was 5, so 144/5 expressed as a mixed fraction is 284/5.
- First, divide the top number by the bottom number.
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7Finished!
41/2 x 62/5 = 284/5
References
- ↑ https://www.cuemath.com/numbers/improper-fractions/
- ↑ https://www.mathsisfun.com/improper-fractions.html
- ↑ https://www.mathsisfun.com/improper-fractions.html
- ↑ https://www.calculatorsoup.com/calculators/math/mixed-number-to-improper-fraction.php
- ↑ https://www.cuemath.com/numbers/multiplying-fractions/
- ↑ https://www.mathsisfun.com/greatest-common-factor.html
- ↑ https://www.cuemath.com/numbers/improper-fraction-to-mixed-number/
Community Q&A
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QuestionWhen simplifying, is it the same way as doing it with any other operation?
Community AnswerIn terms of fractions, yes. You find the greatest common factor, then you factor the fraction/mixed number. -
QuestionHow do I divide mixed numbers?
DonaganTop AnswererTurn each mixed number into an improper fraction, then divide as you would with any fractions. -
QuestionWhat if after Imultiply the improper fraction, the numbers I get don't have any factors in common?
LyKaxandra CaimoyCommunity AnswerIf you are referring to reducing it to lowest term, then that is the simplest form or, otherwise, convert it to mixed numbers.
About This Article
To multiply mixed numbers, start by converting each mixed number to an improper fraction. Then, multiply the improper fractions together. Reduce your answer to the lowest terms using the greatest common factor. Finally, convert your answer back to a mixed number. To learn how to find the greatest common factor to reduce your fraction, keep reading the article!
