Question

How do you divide and write `5\frac { 5} { 8} \div 5\frac { 5} { 14}` as a mixed number in lowest terms?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number to an improper fraction:

`5 5/8 -: 5 5/14 =>`

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

`([8/8 xx 5] + 5/8) -: ([14/14 xx 5] + 5/14) =>`

`(40/8 + 5/8) -: (70/14 + 5/14) =>`

`45/8 -: 75/14`

Next, rewrite the expression as:

`(45/8)/(75/14)`

Now, use this rule for dividing fractions to divide the terms:

`(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)(45)/color(blue)(8))/(color(green)(75)/color(purple)(14)) = (color(red)(45) xx color(purple)(14))/(color(blue)(8) xx color(green)(75)) =>`

`(color(red)(45)/color(blue)(8))/(color(green)(75)/color(purple)(14)) => (color(red)(3 xx 3 xx 5) xx color(purple)(2 xx 7))/(color(blue)(2 xx 4) xx color(green)(3 xx 5 xx 5)) =>`

`(color(red)(color(green)(cancel(color(red)(3))) xx 3 xx color(red)(color(green)(cancel(color(red)(5))))) xx color(purple)(color(blue)(cancel(color(purple)(2))) xx 7))/(color(blue)(color(purple)(cancel(color(blue)(2))) xx 4) xx color(green)(color(red)(cancel(color(green)(3))) xx color(red)(cancel(color(green)(5))) xx 5)) =>`

`(3 xx 7)/(4 xx 5) =>`

`21/20`

We can now convert this to a mixed number:

`21/20 => (20 + 1)/20 => 20/20 + 1/20 => 1 + 1/20 =>`

`1 1/20`