# How do you know if the pair 6/9 and 2/3 form a proportion?

Jul 14, 2016

They are proportions, see explanation.

#### Explanation:

First, set them both equal to each other.

$\frac{6}{9} = \frac{2}{3}$

Then, cross multiply. Follow this method: $\frac{a}{b} = \frac{c}{d}$ = $a d = b c$.

$6 \left(3\right) = 9 \left(2\right)$

$18 = 18$

$18$ does equal $18$, so the two fractions do show a proportion.

Another way to look at is to set both fractions equal and see what happened to one fraction to get to the other.

$\frac{2}{3} = \frac{6}{9}$

$\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

$\frac{6}{9} = \frac{6}{9}$

We found that you can multiply $\frac{3}{3}$ to $\frac{2}{3}$ to get the other fraction or divide $\frac{3}{3}$ from $\frac{6}{9}$ to get the other fraction. These both represent proportions.

Jul 14, 2016

See explanation

#### Explanation:

To investigate if$\text{ "6/9-=2/3" }$ ( $\equiv$ means 'equivalent to')

$\textcolor{b l u e}{\text{Consider the left hand side (LHS)}}$

Using the property of ratios
Divide top and bottom by 3 giving

$\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

$\textcolor{b l u e}{\text{Comparing shows that } L H S \equiv R H S}$

Thus it is true that $\frac{6}{9} \equiv \frac{2}{3}$