Question

What is 3/2÷(1/4+4/7) as a fraction in simplest form?
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Answer 1

1
`(19)/(23)`

Explanation:

`(3)/(2)` ÷ (
`(1)/(4)` +
`(4)/(7)`) Add the fractions together first.

Rewrite them with the common denominator of 28.

`(1)/(4)` +
`(4)/(7)` 4x7 = 28, so multiply the top of the first fraction by 7 to get the equivalent fraction. 7x4 = 28, so multiply the top of the second fraction by 4 to the second equivalent fraction

`(7)/(28)` +
`(16)/(28)` =
`(23)/(28)`

`(3)/(2)` ÷
`(23)/(28)` Which is the same as

`(3)/(2)` x
`(28)/(23)` =
`(84)/(46)` Divide the top and bottom by 2

`(42)/(23)` 23 goes in 42 1 time with 19 left over

1
`(19)/(23)`

Answer 2

1
`(19)/(23)`

Explanation:

`(3)/(2) / ( (1)/(4) + (4)/(7) )`

`(3)/(2) / ( (7 + 16)/(28) )`

`(3)/(2) / (23)/(28)`

Cross Multiply

`(3)/(2) * (23)/(28) = (84)/(46)`

Reduce

`(84)/(46) / (2)/(2) = (42)/(23)`

Divide, set the answer as the whole number and the remainder as the numerator.

1
`(19)/(23)`