# How do you know if the pair 4/3 and 8/6 form a proportion?

Jun 6, 2017

If you divide one into the other and the answer is 1 then they are of the same ratio.

#### Explanation:

Write in faction format $\text{ "4/3"; } \frac{8}{6}$

$\textcolor{b l u e}{\text{The test process}}$

$\frac{4}{3} \div \frac{8}{6}$

$\textcolor{g r e e n}{\frac{4}{3} \times \textcolor{red}{\frac{6}{8}} \text{ "=" "(4xxcolor(red)(6))/(3xxcolor(red)(8))" "=" } \frac{\textcolor{red}{6} \times 4}{3 \times \textcolor{red}{8}}}$

$\text{ "=" "color(green)((color(red)(6))/3xx4/(color(red)(8))" "=" } 2 \times \frac{1}{2}$

$\text{ "=" } 1$
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$\textcolor{b l u e}{\text{A different test}}$

Multiply by 1 and you do not change the value. However, 1 comes in many forms. So you can change the way a proportion or fraction looks without changing its actual value.

color(green)(4/3color(red)(xx1) " "=" "4/3color(red)(xx2/2)" "=" "8/6

Thus it is true that $\frac{4}{3} \equiv \frac{8}{6}$

Where $\equiv$ means 'proportional to'