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Are these ratios equivalent? How do you know?

8/24 and 10/30

1 answer

To determine if the ratios \( \frac{8}{24} \) and \( \frac{10}{30} \) are equivalent, we can simplify both fractions.

Starting with \( \frac{8}{24} \):

  1. Find the greatest common divisor (GCD) of 8 and 24, which is 8.
  2. Divide both the numerator and the denominator by their GCD:

\[ \frac{8 \div 8}{24 \div 8} = \frac{1}{3} \]

Now, simplify \( \frac{10}{30} \):

  1. The GCD of 10 and 30 is 10.
  2. Divide both the numerator and the denominator by their GCD:

\[ \frac{10 \div 10}{30 \div 10} = \frac{1}{3} \]

Since both \( \frac{8}{24} \) and \( \frac{10}{30} \) simplify to \( \frac{1}{3} \), the two ratios are equivalent.

Therefore, \( \frac{8}{24} \) and \( \frac{10}{30} \) are indeed equivalent ratios.