Question

How do you evaluate `4\frac{3}{4}\div 28\frac{1}{2}`?

Answer 1

See a solution process below:

Explanation:

First, convert the mixed numbers to improper fractions:

`4 3/4 -: 28 1/2 =>`

`(4 + 3/4) -: (28 + 1/2) =>`

`([4/4 xx 4] + 3/4) -: ([2/2 xx 28] + 1/2) =>`

`(16/4 + 3/4) -: (56/2 + 1/2) =>`

`(16 + 3)/4 -: (56 + 1)/2 =>`

`19/4 -: 57/2`

Next, rewrite the expression as:

`(19/4)/(57/2)`

Now, 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)(4))/(color(green)(57)/color(purple)(2)) => (color(red)(19) xx color(purple)(2))/(color(blue)(4) xx color(green)(57)) => (cancel(color(red)(19)) xx cancel(color(purple)(2)))/(cancel(color(blue)(4))2 xx cancel(color(green)(57))3) => 1/6`