Question

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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

.1

Multiply the whole number by the denominator of its combined fraction.[1] 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 {\displaystyle 6{\frac {1}{2}}\div 2{\frac {1}{4}}}6{\frac {1}{2}}\div 2{\frac {1}{4}}, you would multiply {\displaystyle 6\times 2=12}6\times 2=12 and {\displaystyle 2\times 4=8}2\times 4=8.

Image titled Divide Mixed Fractions Step 2

2

Add the numerator to the product.[2] Do this for both mixed numbers. This sum will be the numerator of your improper fraction.

For example, {\displaystyle 12+1=13}12+1=13 and {\displaystyle 8+1=9}8+1=9.

Image titled Divide Mixed Fractions Step 3

3

Place the sum over the original denominator.[3] Complete this step for both fractions, making sure you use the correct denominators. These are your improper fractions that you will use to complete the division.

For example, {\displaystyle 6{\frac {1}{2}}}6{\frac {1}{2}} becomes {\displaystyle {\frac {13}{2}}}{\frac {13}{2}} and {\displaystyle 2{\frac {1}{4}}}2{\frac {1}{4}} becomes {\displaystyle {\frac {9}{4}}}{\frac {9}{4}}.

Image titled Divide Mixed Fractions Step 4

4

Convert whole numbers to fractions. 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.[4]

For example, {\displaystyle 3={\frac {3}{1}}}3={\frac {3}{1}}.

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Part 2 of 3:

Dividing Improper Fractions

Image titled Divide Mixed Fractions Step 5

1

Write the new division problem. Use the improper fractions you found by completing the calculations in Part 1.

For example, {\displaystyle {\frac {13}{2}}\div {\frac {9}{4}}}{\frac {13}{2}}\div {\frac {9}{4}}.

Image titled Divide Mixed Fractions Step 6

2

Take the reciprocal of the second fraction.[5] To find a reciprocal of a fraction, you need to “flip” it, so that the numerator becomes the denominator, and the denominator becomes the numerator.[6] Then, change the problem to a multiplication problem.[7] [8]

For example, if you take the reciprocal of {\displaystyle {\frac {9}{4}}}{\frac {9}{4}}, it becomes {\displaystyle {\frac {4}{9}}}{\frac {4}{9}}. So {\displaystyle {\frac {13}{2}}\div {\frac {9}{4}}}{\frac {13}{2}}\div {\frac {9}{4}} becomes {\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}}{\frac {13}{2}}\times {\frac {4}{9}}

Image titled Divide Mixed Fractions Step 7

3

Multiply the numerators. To do this, multiply them as if they were whole numbers. This product will be the numerator of your answer.[9] [10]

For example, if calculating {\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}}{\frac {13}{2}}\times {\frac {4}{9}}, you would multiply the numerators: {\displaystyle 13\times 4=52}13\times 4=52.

Image titled Divide Mixed Fractions Step 8

4

Multiply the denominators. To do this, multiply them as if they were whole numbers. This product will be the denominator of your answer.[11] [12]

For example, if calculating {\displaystyle {\frac {13}{2}}\times {\frac {4}{9}}}{\frac {13}{2}}\times {\frac {4}{9}}, you would multiply the denominators: {\displaystyle 2\times 9=18}2\times 9=18. Putting together your numerator and denominator, your answer becomes {\displaystyle {\frac {52}{18}}}{\frac {52}{18}}.

Image titled Divide Mixed Fractions Step 9

5

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. For more information on this process, read Reduce Fractions.

For example, {\displaystyle 52}52 and {\displaystyle 18}18 are both divisible by {\displaystyle 2} 2.

{\displaystyle 52\div 2=26}52\div 2=26

{\displaystyle 18\div 2=9}18\div 2=9

So, {\displaystyle {\frac {52}{18}}={\frac {26}{9}}}{\frac {52}{18}}={\frac {26}{9}}