Q17. - Algebra 1

Question

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

$\frac{3}{4}$ and $\frac{15}{20}$

Step-by-Step Solution

Answer

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

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 3 4 and 15 20 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”.