How to Divide Mixed Numbers

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Divide mixed numbers & fractions with the help of an expert tutor

Co-authored by David Jia and Luke Smith, MFA

Last Updated: February 13, 2025 Fact Checked

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Converting to Improper Fractions

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Dividing Improper Fractions

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Converting Back to Mixed Fractions

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A mixed number, or mixed fraction, is a number that combines a whole number and a fraction. Dividing two mixed numbers might seem intimidating at first, but it’s actually pretty simple! You just have to convert them into improper fractions first. We talked to math tutor David Jia to show you how to do it from start to finish.

Dividing Mixed Fractions

Convert both mixed numbers to improper fractions by multiplying the denominator by the whole number, then adding it to the numerator. Find the reciprocal of the second fraction by flipping it, then multiply the first improper fraction by this reciprocal.

Part 1

Part 1 of 3:

Converting Mixed Numbers to Improper Fractions

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1
Multiply the whole number by the denominator of the fraction it’s next to. Before we can divide mixed fractions, we need to make it so that they’re just fractions. To do this, we make them improper fractions. First, multiply the denominator, or bottom number, of each mixed number’s fraction by that mixed number’s whole number. ^{[1]
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Research source} Do this for both mixed numbers, and make note of the answers. We’ll keep using them.
- For example, if you wanted to show $6{\frac {1}{2}}\div 2{\frac {1}{4}}$ as improper fractions, you first multiply $6\times 2=12$ and $2\times 4=8$ .
- If the whole number is alone without a fraction, then it’s not a mixed number. In this case, all we need to do is make it a fraction by putting it over 1. For example: $3={\frac {3}{1}}$ .
2
Add the numerator to the product. Now, take the product you just found and add it to the numerator, or top number, of that fraction. ^{[2]
X
Research source} Do this for both mixed numbers. This sum will be the numerator of your improper fraction.
- For example, $12+1=13$ and $8+1=9$ .
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3
Place the sum over the original denominator. Complete this step for both fractions, making sure you use the correct denominators. These are the improper fractions that you will use to complete the division. ^{[3]
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Research source}
- For example, $6{\frac {1}{2}}$ becomes ${\frac {13}{2}}$ and $2{\frac {1}{4}}$ becomes ${\frac {9}{4}}$ .
- Explanation: What we’re actually doing here is making each whole number a fraction, then adding it to the existing fraction to combine the mixed numbers into a single fraction. For example, $2{\frac {1}{4}}$ is the same as ${\frac {4}{4}}+{\frac {4}{4}}+{\frac {1}{4}}$ , we’re just using a shortcut to do the same thing.

Part 2

Part 2 of 3:

Dividing Improper Fractions

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1
Flip the second fraction and make it a multiplication equation. The simplest way to divide two fractions is to find the reciprocal of the second fraction, then multiply instead of divide. To find a reciprocal of a fraction, you simply “flip” it so that the numerator becomes the denominator, and the denominator becomes the numerator. ^{[4]
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Research source} Then, change the problem to a multiplication problem, Jia tells us. ^{[5]
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Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021.}
- For example, if you take the reciprocal of ${\frac {9}{4}}$ , it becomes ${\frac {4}{9}}$ . So ${\frac {13}{2}}\div {\frac {9}{4}}$ becomes ${\frac {13}{2}}\times {\frac {4}{9}}$
2
Multiply the numerators. To do this, multiply them straight across as if they were whole numbers. This product will be the numerator of your answer, says Jia. ^{[6]
X
Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021.}
- For example, if calculating ${\frac {13}{2}}\times {\frac {4}{9}}$ , you would multiply the numerators: $13\times 4=52$ .
3
Multiply the denominators. To do this, multiply them as if they were whole numbers, going straight across. This product will be the denominator of your answer, Jia says. ^{[7]
X
Expert Source

David Jia
Academic Tutor

Expert Interview. 23 February 2021.}
- For example, if calculating ${\frac {13}{2}}\times {\frac {4}{9}}$ , you would multiply the denominators: $2\times 9=18$ . Putting together your numerator and denominator, your answer becomes ${\frac {52}{18}}$ .
4
Simplify your answer, if possible. To simplify , or reduce, a fraction, you need to find the greatest factor (besides 1) that is common to the numerator and the denominator. Then, divide the numerator and denominator by that factor. ^{[8]
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Research source}
- For example, $52$ and $18$ are both divisible by $2$ .
  $52\div 2=26$
  $18\div 2=9$
  So, ${\frac {52}{18}}={\frac {26}{9}}$
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

Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.

Part 3

Part 3 of 3:

Converting Improper Fractions Back Into Mixed Numbers

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1
Divide the numerator by the denominator. If there is no remainder, then your answer is a whole number rather than a mixed number, and you don’t need to do anything else. Usually, though, you will have a remainder. Set this aside for now. The quotient you found when dividing the numerator by the denominator will be the whole number of your mixed number. ^{[9]
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Research source}
- For example, $26\div 9=2$ with a remainder of $8$ . Thus, the whole number of your mixed number will be $2$ .
2
Turn the remainder into the numerator of your fraction. Place this numerator over the denominator you found by simplifying the fraction in the last steps. This will give you the fraction of your mixed number. ^{[10]
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Research source}
- For example, if your previous denominator is $9$ and your remainder is $8$ , the fraction of your mixed number is ${\frac {8}{9}}$ .
Now, put the whole number you found by dividing the numerator by the denominator next to the fraction you just calculated. This gives you the final answer to your original division problem. ^{[11]
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Research source}

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How do I calculate 2 5/7 divided by 3 1/2?

Donagan

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Change both mixed numbers to improper fractions. Invert the second improper fraction, then multiply it by the first fraction to get the answer. Reduce it if possible, and convert it to a mixed number if desired.

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To find the reciprocal, I flip the second fraction. What if I have fraction divided by fraction divided by fraction? Would I flip the last fraction, or the second one?

Donagan

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Flip both the second and third fractions.

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Why do you flip the fractions and then multiply in Part 2, step 2?

Community Answer

Any fraction multiplied by its reciprocal is equal to 1. For example, 5/10 x 10/5 = 50/50 = 1. When you divide by a fraction, you want to cancel the second fraction by changing it to a 1. So, to do this, you have to multiply it by its reciprocal (or flip it). But, if you're going to multiply the second fraction by its reciprocal, you also have to multiply the other number by its reciprocal. So when you "flip and multiply" you are really cancelling out the second fraction, which leaves you with just multiplying the first fraction by the second fraction's reciprocal.

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How to Divide Mixed Numbers

Dividing Mixed Fractions

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Converting Mixed Numbers to Improper Fractions

Dividing Improper Fractions

Converting Improper Fractions Back Into Mixed Numbers

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