Question

Are these ratios equivalent? $70 for every 72 kilograms $92 for every 73 kilograms

Answer 1

To determine whether the ratios are equivalent, we can express both ratios in fractional form and compare them.

First, we represent the ratios:

1. The first ratio is \( \frac{70}{72} \).
2. The second ratio is \( \frac{92}{73} \).

Next, we will simplify each fraction starting with the first ratio:

\[
\frac{70}{72}
\]

The greatest common divisor (GCD) of 70 and 72 is 2. We divide both the numerator and the denominator by 2:

\[
\frac{70 \div 2}{72 \div 2} = \frac{35}{36}
\]

Now, we simplify the second ratio:

\[
\frac{92}{73}
\]

The GCD of 92 and 73 is 1 (since 73 is prime and does not divide 92). Therefore, this fraction is already in its simplest form:

\[
\frac{92}{73}
\]

Now we will determine if \( \frac{35}{36} \) is equivalent to \( \frac{92}{73} \) by cross-multiplying:

Calculate:

\[
35 \times 73 \quad \text{and} \quad 36 \times 92
\]

Calculating \( 35 \times 73 \):

\[
35 \times 73 = 2555
\]

Calculating \( 36 \times 92 \):

\[
36 \times 92 = 3312
\]

Now we compare the two products:

- \( 35 \times 73 = 2555 \)
- \( 36 \times 92 = 3312 \)

Since \( 2555 \neq 3312 \), we conclude that:

\[
\frac{70}{72} \neq \frac{92}{73}
\]

Thus, the ratios are **not equivalent**.