Q16 - Algebra 1

Question

Use cross products to determine whether each pair of ratios forms a proportion. Write yes or no.

$\frac{2}{3}$ and $\frac{4}{9}$

Step-by-Step Solution

Answer

The given pair of ratios does not form a proportion. So, final answer is “no”.

Step 1. Define a ratio.

The ratio of the two numbers x and y is defined as $x:y=\frac{x}{y}$, where, $y\ne 0$.

Step 2. Use cross products to determine whether the pair of ratios a b and c d forms a proportion.

The pair of ratio $\frac{a}{b}$ and $\frac{c}{d}$ forms a proportion if, $a.d=b.c$.

Step 3. Use cross products to determine whether the pair of ratios 2 3 and 4 9 forms a proportion.

Cross multiply the numbers.

$\begin{array}{c}2\times 9=18\\ 3\times 4=12\end{array}$

Since, $18\ne 12$

Hence, the ratios $\frac{2}{3}$ and $\frac{4}{9}$ are not in proportion.

 

Therefore, the given pair of ratios does not form a proportion. So, final answer is “no”.