Question

How do you evaluate `(\frac { 5a } { 3b } ) \div ( \frac { 15c } { 9a ^ { 2} } )`?

Answer 1

See a solution process belowL

Explanation:

First, rewrite the expression as:

`((5a)/(3b))/((15c)/(9a^2))`

Now, use this rule for dividing fractions to evaluate the expression:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(5a)/color(blue)(3b))/(color(green)(15c)/color(purple)(9a^2)) =>`

`(color(red)(5a) xx color(purple)(9a^2))/(color(blue)(3b) xx color(green)(15c)) =>`

`(color(red)(color(black)(cancel(color(red)(5)))a) xx color(purple)(color(black)(cancel(color(purple)(9)))3a^2))/(color(blue)(color(black)(cancel(color(blue)(3)))b) xx color(green)(color(black)(cancel(color(green)(15)))3c)) =>`

`(3a^3)/(3bc) =>`

`(color(red)(cancel(color(black)(3)))a^3)/(color(red)(cancel(color(black)(3)))bc) =>`

`a^3/(bc)`

Answer 2

`a^3/(bc)`

Explanation:

Lets split this into two parts. Numbers and letters (variables)

`color(blue)("Dealing with the numbers.")`

`5/3-:15/9` It gives the wrong answer if you cancel out at this stage.

Write as

`5/3xx9/15 larr" Now you can cancel"`

I am swapping things round to make the cancelling more obvious

`5/15xx9/3`

`1/3xx3/1=1`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Dealing with the variable.")`

`a/b-:c/a^2`

`a/bxxa^2/c = a^3/(bc)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together.")`

`1xxa^3/(bc) = a^3/(bc)`