Question

How do you divide `2\frac { 5} { 7} \div \frac { 3} { 2}`?

Answer 1

`38/21`

Explanation:

First, change the mixed number into an improper fraction.

For `2 5/7`, that's

`((7*2) +5)/7 = 19/7`

Then you flip the second fraction and add a `xx` sign, so

`19/7 xx 2/3`

Multiply the top and bottom numbers

`38/21`

Hope this helps!

Answer 2

`2 5/7-:3/2=color(blue)(38/21=1 17/21`

Explanation:

Divide:

`2 5/7-:3/2`

First convert `2 5/7` to an improper fraction. Multiply the denominator by the whole number and then add the numerator. Place this over the denominator `7`.

`2 5/7=((7xx2+5))/7`

`2 5/7=19/7`

Rewrite the expression.

`19/7-:3/2`

When dividing by a fraction, invert it and multiply.

`19/7xx2/3`

Multiply the numerators and denominators across.

`(19xx2)/(7xx3)`

Simplify.

`38/21`

`38/21` can be converted to a mixed number.

Using long division, divide `38` by `21` to get the whole number quotient with a remainder. The whole number quotient becomes the whole number of the mixed number, the remainder becomes the numerator, and the divisor `21` is the denominator.

`38-:21="1 remainder 17"`

`38/21=1 17/21`