Question

How do you multiply `(2a)/(7b^3)div(10a^5)/77`?

Answer 1

`11/(5a^4b^3)`

Explanation:

To change division to multiplication , in fractions, we take the 'reciprocal' (turn fraction upside down) of the divisor.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a/b ÷c/d=a/bxxd/c)color(white)(a/a)|)))`

`rArr(2a)/(7b^3)÷(10a^5)/(77)=(2a)/(7b^3)xx(77)/(10a^5)`

Now that we are multiplying the 2 fractions we can cancel any common factors on the numerators/denominators.

`(cancel(2)^1 color(red)cancel(a)^1)/(color(blue)cancel(7)^1 b^3)xx(color(blue)cancel(77)^(11))/(cancel(10)^5color(red)cancel(a^5)^4)=(1xx1xx11)/(1xxb^3xx5xxa^4)`

`rArr(2a)/(7b^3)÷(10a^5)/(77)=11/(5a^4b^3`