Question

How do you divide `-\frac { 7} { 8} \div \frac { 7} { 12}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`((-7)/8)/(7/12)`

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)(-7)/color(blue)(8))/(color(green)(7)/color(purple)(12)) => (color(red)(-7) xx color(purple)(12))/(color(blue)(8) xx color(green)(7)) => -(cancel(color(red)(-7)) xx color(purple)(12))/(color(blue)(8) xx cancel(color(green)(7))) => (-12)/8 =>`

`(4 xx -3)/(4 xx 2) => (color(red)(cancel(color(black)(4))) xx -3)/(color(red)(cancel(color(black)(4))) xx 2) =>`

`-3/2`

Answer 2

`-3/2`

Explanation:

Dividing by a fraction is the same as multiply by its reciprocal.

`-7/8 color(blue)(div 7/12)`

`= -7/8 color(blue)(xx 12/7)`

Notice that multiplying by `12` converts the first fraction into twelfths, while dividing by `7`, determines how many groups of `7` can be made with the twelfths.

`-cancel7/cancel8^2 xx cancel12^3/cancel7" "larr` cancel where possible

`-3/2`

The entire answer is negative because a negative number multiplied by a positive number gives a negative.