Question

How do you evaluate `\frac { \frac { 1} { 2} + \frac { 8} { 7} } { \frac { 3} { 2} - \frac { 4} { 7} }`?

Answer 1

See a solution process below:

Explanation:

First, we need to combine the fractions in the numerator and denominator by putting the over common denominators and then adding or subtracting them:

`(1/2 + 8/7)/(3/2 - 4/7) => ((7/7 xx 1/2) + (2/2 xx 8/7))/((7/7 xx 3/2) - (2/2 xx 4/7)) => (7/14 + 16/14)/(21/14 - 8/14) =>`

`((7 + 16)/14)/((21 - 8)/14) => (23/14)/(13/14)`

We can 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)(23)/color(blue)(14))/(color(green)(13)/color(purple)(14)) = (color(red)(23) xx color(purple)(14))/(color(blue)(14) xx color(green)(13)) = (color(red)(23) xx cancel(color(purple)(14)))/(cancel(color(blue)(14)) xx color(green)(13)) = 23/13`