Question

How do you divide `2\frac { 5} { 7} \div 3\frac { 5} { 8}`?

Answer 1

See a solution process below:

Explanation:

First, convert the mixed numbers into improper fractions:

`(2 + 5/7) -: (3 + 5/8) =>`

`([7/7 xx 2] + 5/7) -: ([8/8 xx 3] + 5/8) =>`

`(14/7 + 5/7) -: (24/8 + 5/8) =>`

`(14 + 5)/7 -: (24 + 5)/8 =>`

`19/7 -: 29/8`

Next, rewrite the expression as:

`(19/7)/(29/8)`

Then, use this rule for dividing fractions:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(19)/color(blue)(7))/(color(green)(29)/color(purple)(8)) => (color(red)(19) xx color(purple)(8))/(color(blue)(7) xx color(green)(29)) => 152/203`