Question

Are the ratios $15:3$ and $5:1$ equivalent?

• A. Yes
• B. No
• C. Cannot be determined

Answer 1

The correct option is A Yes

To determine whether two ratios are equivalent, write them as simplified fractions. If the simplified fractions are equal, then the ratios are equivalent.

Write the ratio as a fraction by writing the antecedent of the ratio as the numerator, and the consequent of the ratio as the denominator.
$15:3\to \frac{15}{3}$
$5:1\to \frac{5}{1}$

Here, the denominators are 3 and 1.

Now, rewrite $\frac{5}{1}$ with a denominator of 3 by multiplying its numerator and denominator by 3.
$\frac{5}{1}=\frac{5\times 3}{1\times 3}=\frac{15}{3}$
$\text{So,}\frac{15}{3}\text{and}\frac{5}{1}\text{are equal.}$
$\therefore 15:3\text{and}5:1\text{are equivalent.}$