Question

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

$\frac{3}{4}$and$\frac{15}{20}$

Short answer

The given pair of ratios forms a proportion. So, final answer is “yes”.

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 34 and 1520 forms a proportion.

Cross multiply the numbers.

$\begin{array}{c}3\times 20=60\\ 4\times 15=60\end{array}$

Since, $60=60$

Hence, the ratios $\frac{3}{4}$and $\frac{15}{20}$are not in proportion.

Therefore, the given pair of ratios forms a proportion. So, final answer is “yes”.