Question

How do you simplify `(2/15)(25/49)(-63/72)`?

Answer 1

`-5/84`

Explanation:

`"note that "-63/72" can be simplified"`

`"by "color(blue)"cancelling "" numerator/denominator by 9"`

`rArr-63/72=-cancel(63)^7/cancel(72)^8=-7/8`

`"thus the calculation becomes"`

`2/15xx25/49xx-7/8`

`"simplify further by cancelling 2/8, 15/25 and 7/49"`

`cancel(2)^1/cancel(15)^3xxcancel(25)^5/cancel(49)^7xx-cancel(7)^1/cancel(8)^4`

`"multiply the remaining values on the "`
`"numerator/denominator"`

`=(1xx5xx-1)/(3xx7xx4)=-5/84`

Answer 2

`-5/84`

Explanation:

Start by cancelling with any common factors in the numerators and denominators.

`2/15 xx25/49 xx-63/72`

`div 5 (15 and 25)and div 7 (49 and 63)`

`=-2/cancel15^3 xxcancel25^5/cancel49^7 xxcancel63^9/72`

`=-cancel2/3 xx5/7 xxcancel9/(cancel72^(cancel8^4))`

`div 9 (9 and 72) and div 2 (2 and 8)`

`=5/(3xx7xx4)`

`= -5/(84)`

There are different ways of cancelling. The order is not important.

This is easier than multiplying all the tops together and all the bottoms together and then trying to simplify.