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

##### 1 Answer
Mar 6, 2017

$\frac{5}{2}$

#### Explanation:

There are 2 possible approaches to evaluating this product.

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

To simplify consider $\textcolor{b l u e}{\text{common factors}}$ of the values on the numerators with values on the denominators and $\textcolor{b l u e}{\text{cancel}}$

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

$\Rightarrow {\cancel{\textcolor{red}{7}}}^{1} / {\cancel{\textcolor{m a \ge n t a}{3}}}^{1} \times {\cancel{\textcolor{m a \ge n t a}{15}}}^{5} / {\cancel{\textcolor{red}{14}}}^{2} \leftarrow \text{ cancelling}$

$= \frac{1 \times 5}{1 \times 2}$

$= \frac{5}{2} \leftarrow \textcolor{p u r p \le}{\text{ in simplest form}}$

• color(red)" Multiply then simplify"

$\frac{7}{3} \times \frac{15}{14} = \frac{7 \times 15}{3 \times 14} = \frac{105}{42}$

If you see that 21 is the $\textcolor{b l u e}{\text{highest common factor}}$ then straight to the simplification.

$\frac{105}{42} = {\cancel{105}}^{5} / {\cancel{42}}^{2} = \frac{5}{2}$

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

$\Rightarrow {\cancel{105}}^{35} / {\cancel{42}}^{14} = {\cancel{35}}^{5} / {\cancel{14}}^{2} = \frac{5}{2} \leftarrow \textcolor{p u r p \le}{\text{ in simplest form}}$

A fraction is in $\textcolor{p u r p \le}{\text{simplest form}}$ when no other factor but 1 will divide into the numerator/denominator.