Question

How do you multiply and simplify `\frac { 79n } { 25} \cdot \frac { 85} { 27n ^ { 2} }`?

Answer 1

`1343/(135n)`

Explanation:

To multiply fractions you multiply then numerator by the numerator and the denominator by the denominator and then factor. Or factor first and then multiply.

`(79n*85)/(25*27n^2) =>`

`(6715n)/(675n^2) =>`

`1343/(135n) (5n)/(5n) =>`

`1343/(135n) * 1 =>`

`1343/(135n)`

Answer 2

`=1343/(135n)`

Explanation:

When multiplying with fractions you can simplify (cancel) any numerator with any denominator as long as there is a multiplication between them.
Cancelling first means the numbers stay small enough to work with without having to simplify unwieldy fractions.

`(79n)/25 xx 85/(27n^2)" "larr` 25 and 85 have a factor of 5.

`=(79n)/cancel25^5 xx cancel85^17/(27n^2)`

79 and 17 are both prime numbers, so no further cancelling is possible.

`=(1343n)/(135n^2)" "larr`subtract the indices of the variables

`=1343/(135n)`