Question

How do you multiply `\frac { 9} { 14} \cdot \frac { 4} { 27}`?

Answer 1

`2/7`

Explanation:

To multiply fractions:

• Change any mixed numbers to improper fractions.
• Cancel any like factors in numerator and denominator
• Multiply straight across
• simplify if possible

`9/14 xx 4/27`

recall that the prime factors are:

`(3xx3)/(2xx7) xx (2xx2)/(3xx3xx3)`

`=(cancel3xxcancel3)/(cancel2xx7) xx (cancel2xx2)/(cancel3xxcancel3xx3)" "larr`cancel like factors

`= 2/21`

You can also just cancel using the times tables without resorting to prime factors

`cancel9/cancel14^7 xx cancel4^2/cancel27" "`(divide 4 and 14 by 2 and divide 9 into 27)

`=2/7`

Answer 2

See a solution process below:

Explanation:

First, factor and cancel common terms in the numerator and denominator:

`9/14 * 4/27 => 9/(2 * 7) * (2 * 2)/(9 * 3) => color(red)(cancel(color(black)(9)))/(color(blue)(cancel(color(black)(2))) * 7) * (color(blue)(cancel(color(black)(2))) * 2)/(color(red)(cancel(color(black)(9)) * 3)) => 1/7 * 2/3`

Now, to multiply fractions we multiply the numerators over the denominators also multiplied:

`1/7 * 2/3 => (1 * 2)/(7 * 3) => 2/21`