Question

How do you evaluate `1\frac { 9} { 10} \div 4\frac { 1} { 4}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite each of the mixed numbers as an improper fraction:

`1 9/10 = 1 + 9/10 = (10/10 xx 1) + 9/10 = 10/10 + 9/10 = (10 + 9)/10 = 19/10`

`4 1/4 = 4 + 1/4 = (4/4 xx 4) + 1/4 = 16/4 + 1/4 = (16 + 1)/4 = 17/4`

We can now rewrite this problem as:

`1 9/10 -: 4 1/4 => 19/10 -: 17/4 => (19/10)/(17/4)`

We can now use this rule for dividing fractions to evaluate the expression:

`(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)(10))/(color(green)(17)/color(purple)(4)) =>`

`(color(red)(19) xx color(purple)(4))/(color(blue)(10) xx color(green)(17)) =>`

`(color(red)(19) xx color(purple)((2 xx 2)))/(color(blue)((2 xx 5)) xx color(green)(17)) =>`

`(color(red)(19) xx color(purple)((cancel(2) xx 2)))/(color(blue)((cancel(2) xx 5)) xx color(green)(17)) =>`

`38/85`