Question

What is the quotient in simplest form?

3/4 divided by 5/16
15/64
15/16
2 2/5
2 8/20

Answer 1

2 2/5

Explanation:

The quotient means the answer to a division problem.

`(3)/(4) / (5)/(16)`

Flip the second fraction's top and bottom. This becomes a multiplication problem.

`=(3)/(4) * (16)/(5)` Multiply the two numerators, multiply the two denominators

`=(3*16)/(4*5)` Simplify

`=(48)/(20)` Reduce this fraction. Top and bottom are divisible by 4.

`=(12)/(5)` This is an improper fraction (top number is greater than bottom)

12/5 is not an option, so we can change it to a mixed fraction, which we take out a whole number (written bigger beside the fraction).

One whole number is worth "5" in the numerator.

`(12)/(5)`

`=(5+5+2)/(5)` Separate the numerator to find how many wholes there are

`=2(2)/(5)` There were two "5"s, so two wholes. It leaves 2 in the numerator.