Question

Calculate the quotient of each expression. Write your answers in lowest terms

Answer 1

1) The quotient is
`{1} (1)/(2)`

2) The quotient is
`(6)/(7) / (7)/(3) =(18)/(49)`

3) The quotient is

Explanation:

1) Given
`(3)/(7) / (2)/(7)`

When dividing whole numbers and fractions, you first change the operation to multiplication and then change the divisor to its reciprocal. The same rule applies to dividing a fraction by another fraction.

ie,
`(3)/(7) / (2)/(7) = (3)/(7) * (7)/(2)` (multiply the fractions)

`(3)/(7) / (2)/(7) =(3)/(2)`

Next, simply the fraction.Now Convert the improper fraction into a mixed number
`1 \frac{1} {2}`

Therefore the quotient is
`1(1)/(2)`

2) Given
`(6)/(7) / 2(1)/(3)`

To find
`(6)/(7) / 2(1)/(3)`

First, write the mixed numbers as improper fractions.

So, the expression becomes

`2(1)/(3)= (7)/(3)` now the given expression may be written as

`(6)/(7) / (7)/(3) = (6)/(7) * (3)/(7)` (multiply the fractions)

`(6)/(7) / (7)/(3) =(18)/(49)`

Next, simply the fraction.Now Convert the improper fraction into a mixed number
`1(1)/(2)`

Multiply by the reciprocal of 65 , which is 56 .

136÷65=136⋅56

Multiply the numerators and multiply the denominators.

=6536

Write the improper fraction as a mixed number.

=12936

So,

216÷115=12936