Question

Question #8e30a

Answer 1

`9/6125`

Explanation:

`color(blue)("Dealing with a lot of those zeros")`

What follows is where the shortcut of cancelling comes from.

`72000 -> 72xx1000`

`4900000-> 4900xx1000`

`(72xx1000)/(4900xx1000)" "=" "72/4900xx1000/1000`

But `1000/1000=1` and anything multiplied by 1 does not change its value.

`72/4900xx1000/1000" "=" "72/4900xx1" "=" "72/4900`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Dealing with what is left")`

`72/4900" "=" "(72-:8)/(49000-:8) = 9/6125`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("This is one way to find a common factor - there are other methods")`

Observe that the highest `ul("common")` factor is `2xx2xx2=8`