Question

How do you divide `\frac { 2z - 14} { 49} \div \frac { z - 7} { 21}`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite this expression as:

`((2z - 14)/49)/((z - 7)/21)`

Then use this rule for dividing fractions as the next step:

`(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)(2z - 14)/color(blue)(49))/(color(green)(z - 7)/color(purple)(21)) = ((color(red)(2z - 14)) xx color(purple)(21))/(color(blue)(49) xx (color(green)(z - 7))) = (21(2z - 14))/(49(z - 7))`

We can next factor several of the terms:

`(21(2z - 14))/(49(z - 7)) = ((7 xx 3)(2(z - 7)))/((7 xx 7)(z - 7))`

We can then cancel several of the common terms in the numerator and the denominator:

`((color(red)(cancel(color(black)(7))) xx 3)(2color(blue)(cancel(color(black)((z - 7))))))/(((color(red)(cancel(color(black)(7))) xx 7)color(blue)(cancel(color(black)((z - 7)))))` `= (3 xx 2)/7 = 6/7`