Question

Are these ratios equivalent? $38 : 10 items $19 : 5 items

Answer 1

To determine if the ratios \( 38 : 10 \) and \( 19 : 5 \) are equivalent, we can express both ratios as fractions and simplify them.

1. The first ratio \( 38 : 10 \) can be expressed as the fraction:
\[
\frac{38}{10}
\]

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{38 \div 2}{10 \div 2} = \frac{19}{5}
\]

2. The second ratio \( 19 : 5 \) can be expressed as the fraction:
\[
\frac{19}{5}
\]

Now, we can see that after simplifying the first ratio, both ratios yield:
\[
\frac{38}{10} = \frac{19}{5}
\]
and
\[
\frac{19}{5} = \frac{19}{5}
\]

Since both ratios simplify to the same fraction, we conclude that:

\[
38 : 10 \text{ is equivalent to } 19 : 5
\]

Thus, we can confirm that the answer is \(\boxed{\text{Yes}}\), the ratios are equivalent.