Question

How do you evaluate `\frac { 3} { 7} \times \frac { 4} { 15}`?

Answer 1

`3/7xx4/15=color(blue)(4/35`

Refer to the explanation for the process.

Explanation:

Evaluate the expression:

`3/7xx4/15`

When multiplying fractions, multiply the numerators and the denominators across, then reduce the resulting fraction if possible.

`(3xx4)/(7xx15)`

Simplify.

`12/105`

Reduce the fraction by dividing the numerator and denominator by `3`.

`(12-:3)/(105-:3)`

`4/35`

Answer 2

`4/35`

Explanation:

When multiplying fractions:

• change mixed numbers to improper fractions
• cancel any common factors if possible
• multiply straight across.

`3/7 xx4/15" "larr 15 = 3xx5`

`cancel3/7 xx4/cancel15^5`

`= 4/35`

Cancelling first means that the numbers are smaller and therefore easier to work with.

If you can as far as possible then you never need to simplify the final answer.