Question

How do you multiply `-\frac { 9} { 25} ( \frac { 5} { 21} )`?

Answer 1

`-3/35`

Explanation:

We have

`-9/25(5/21)`

First off, the negative sign is simply `(-1)` and it is being multiplied by the fraction. The negative sign will be a part of the answer at the end, whether we choose to write it as simply a negative sign or as a negative one. I'll leave it as a negative sign for ease.

When we multiply fractions, we multiply numerators and we multiply denominators:

`-(9xx5)/(25xx21)`

At this point we could go ahead and perform the multiplications and the subsequent divisions, but we can do some cancellations first. Let's see that we can rewrite 25, 21, and 9 as products of their factors:

`-(3xx3xx5)/(5xx5xx7xx3)`

We can reorder this a bit:

`-(3xx5xx3)/(3xx5xx5xx7)=-(3/3)(5/5)(3/(5xx7))=-(1)(1)(3/35)=-3/35`

Answer 2

`-3/35`

Explanation:

`-9/25(5/21)`

`:.=-cancel9^3/cancel25^5 xx cancel5^1/cancel21^7`

`:.=-3/5 xx1/7`

`:.=-3/35`