Question

Are these ratios equivalent?
27 teachers to 30 students
18 teachers to 20 students

Answer 1

To determine if the ratios are equivalent, we can compare them mathematically.

The first ratio is 27 teachers to 30 students, which can be expressed as:

\[
\frac{27}{30}
\]

The second ratio is 18 teachers to 20 students, which can be expressed as:

\[
\frac{18}{20}
\]

Now, let's simplify both ratios:

1. For the first ratio \(\frac{27}{30}\):

\[
\frac{27}{30} = \frac{9}{10} \quad \text{(dividing both the numerator and denominator by 3)}
\]

2. For the second ratio \(\frac{18}{20}\):

\[
\frac{18}{20} = \frac{9}{10} \quad \text{(dividing both the numerator and denominator by 2)}
\]

Since both ratios simplify to \(\frac{9}{10}\), we can conclude that:

\[
\frac{27}{30} = \frac{18}{20}
\]

Therefore, the ratios 27 teachers to 30 students and 18 teachers to 20 students are equivalent.