Question

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

$\frac{2}{3}$and $\frac{4}{9}$

Short answer

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

Step-by-step solution

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 ab and cd 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 23 and 49 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”.