Question

How do you evaluate `\frac { 7} { 3} \cdot \frac { 15} { 14}`?

Answer 1

`5/2`

Explanation:

There are 2 possible approaches to evaluating this product.

`• color(red)" Simplify then multiply"larr" preferable method"`

To simplify consider `color(blue)"common factors"` of the values on the numerators with values on the denominators and `color(blue)"cancel"`

In this case 7 and 14 can be divided by 7 and 3 and 15 by 3

`rArrcancelcolor(red)(7)^1/cancelcolor(magenta)(3)^1xxcancelcolor(magenta)(15)^5/cancelcolor(red)(14)^2larr" cancelling"`

`=(1xx5)/(1xx2)`

`=5/2larrcolor(purple)" in simplest form"`

`• color(red)" Multiply then simplify"`

`7/3xx15/14=(7xx15)/(3xx14)=105/42`

If you see that 21 is the `color(blue)"highest common factor"` then straight to the simplification.

`105/42=cancel(105)^5/cancel(42)^2=5/2`

If not then simplify in steps using 3 then 7, for example.

`rArrcancel(105)^(35)/cancel(42)^(14)=cancel(35)^5/cancel(14)^2=5/2larrcolor(purple)" in simplest form"`

A fraction is in `color(purple)"simplest form"` when no other factor but 1 will divide into the numerator/denominator.