How to Divide Mixed Fractions

Step-by-Step Guide

1. 1

   Step 1: Multiply the whole number by the denominator of its combined fraction.Do this for both mixed numbers.

   Set these products aside.
   
   They are only part of your new numerator.
   
   For example, if you want to calculate 612÷214{\displaystyle 6{\frac {1}{2}}\div 2{\frac {1}{4}}}, you would multiply 6×2=12{\displaystyle 6\times 2=12} and 2×4=8{\displaystyle 2\times 4=8}.
2. 2

   Step 2: Add the numerator to the product.Do this for both mixed numbers.

   This sum will be the numerator of your improper fraction. for For example, 12+1=13{\displaystyle 12+1=13} and 8+1=9{\displaystyle 8+1=9}. , These are your improper fractions that you will use to complete the division.
   
   For example, 612{\displaystyle 6{\frac {1}{2}}} becomes 132{\displaystyle {\frac {13}{2}}} and 214{\displaystyle 2{\frac {1}{4}}} becomes 94{\displaystyle {\frac {9}{4}}}. , If you are working with any whole numbers, you need to convert them to fractions.
   
   To do this, turn the number into the numerator of a fraction.
   
   The denominator will be
   1.
   
   For example, 3=31{\displaystyle 3={\frac {3}{1}}}. , Use the improper fractions you found by completing the calculations in Part
   1.
   
   For example, 132÷94{\displaystyle {\frac {13}{2}}\div {\frac {9}{4}}}. , For example, if you take the reciprocal of 94{\displaystyle {\frac {9}{4}}}, it becomes 49{\displaystyle {\frac {4}{9}}}.
   
   So 132÷94{\displaystyle {\frac {13}{2}}\div {\frac {9}{4}}} becomes 132×49{\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}} , To do this, multiply them as if they were whole numbers.
   
   This product will be the numerator of your answer.
   
   For example, if calculating 132×49{\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}}, you would multiply the numerators: 13×4=52{\displaystyle 13\times 4=52}. , To do this, multiply them as if they were whole numbers.
   
   This product will be the denominator of your answer.
   
   For example, if calculating 132×49{\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}}, you would multiply the denominators: 2×9=18{\displaystyle 2\times 9=18}.
   
   Putting together your numerator and denominator, your answer becomes 5218{\displaystyle {\frac {52}{18}}}. , 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.
   
   For more information on this process, read Reduce Fractions.
   
   For example, 52{\displaystyle 52} and 18{\displaystyle 18} are both divisible by 2{\displaystyle 2}.52÷2=26{\displaystyle 52\div 2=26}18÷2=9{\displaystyle 18\div 2=9}So, 5218=269{\displaystyle {\frac {52}{18}}={\frac {26}{9}}} , If there is no remainder, then your answer is a whole number rather than a mixed number, and you need not do anything further.
   
   Likely, 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.
   
   For example, 26÷9=2{\displaystyle 26\div 9=2} with a remainder of 8{\displaystyle 8}.
   
   Thus, the whole number of your mixed number will be
   2. , Place this numerator over the original denominator.
   
   This will give you the fraction of your mixed number.
   
   For example, if your original denominator is 9{\displaystyle 9} and your remainder is 8{\displaystyle 8}, the fraction of your mixed number is 89{\displaystyle {\frac {8}{9}}}. , This gives you the final answer to your original division problem.
3. 3

   Step 3: Place the sum over the original denominator.Complete this step for both fractions

4. 4

   Step 4: making sure you use the correct denominators.

5. 5

   Step 5: Convert whole numbers to fractions.

6. 6

   Step 6: Write the new division problem.

7. 7

   Step 7: Take the reciprocal of the second fraction.To find a reciprocal of a fraction

8. 8

   Step 8: you need to “flip” it

9. 9

   Step 9: so that the numerator becomes the denominator

10. 10

    Step 10: and the denominator becomes the numerator.Then

11. 11

    Step 11: change the problem to a multiplication problem.

12. 12

    Step 12: Multiply the numerators.

13. 13

    Step 13: Multiply the denominators.

14. 14

    Step 14: Simplify your answer

15. 15

    Step 15: if possible.

16. 16

    Step 16: Divide the numerator by the denominator.

17. 17

    Step 17: Turn the remainder into the numerator of your fraction.

18. 18

    Step 18: Combine the whole number and the fraction.

Detailed Guide

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