This is the complete solutions and answers to the Practice Test on Division of Fractions. If you are not familiar with the method, or you have forgotten how to do it, please read “How to Divide Fractions.“
In dividing fractions, you must convert all mixed fractions to improper fractions before performing the division. The division involves getting the reciprocal (multiplicative inverse) of the divisor, and then multiplying both fractions instead of dividing them.
We get the reciprocal of and multiply it to . The reciprocal of is . So,
(you can use cancellation to do this quickly). Reducing to lowest terms by dividing both the numerator and denominator by 2 results to . Converting this improper fraction to mixed form, we get .
The division is the same as
Reducing to lowest terms by dividing both the numerator and the denominator of the preceding fraction by , we get or .
Any whole number in multiplication has a denominator , so
The reciprocal of is . Now, we multiply:
Dividing both the numerator and denominator by , gives as the lowest term.
We get the reciprocal of , we multiply:
Converting the improper fraction to mixed fraction gives us .
First we convert the mixed fraction to improper fraction, then multiply it to the reciprocal of . If we convert to mixed fraction, we have .
We now multiply:
Converting to mixed form gives us .
Converting to mixed fractions gives us . Now, multiplying to the reciprocal of .
Converting to improper fraction gives us . Now, converting to improper gives us . Now, multiplying to the reciprocal of , we have
The given above is the same as . Now, converting to improper fraction results to . Now, we multiply this result to the reciprocal of which is .
The fraction in improper form is . We multiply it to the reciprocal of .
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