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Ratios and proportions

# Identify equivalent ratios

Two ratios are equivalent if their cross products are equal.

Are these ratios equivalent?

$\fs2\frac{3}{5}=\frac{12}{20}\;\Rightarrow\;3\;\text\;x\;20=5\;\text\;x\;12\;\Rightarrow\;60=60$

The cross products are equal, so the ratios are equivalent.

Are these ratios equivalent?

3 to 5 and 6 to 10

Write the ratios as fractions.

$\frac{3}{5}$ and $\frac{6}{10}$

Compare the two cross products. Multiply the numerator of one fraction and the denominator of the other.

 3 × 10 ? = 5 × 6 30 = 30

The cross products are equal, so the ratios are equivalent.

Are these ratios equivalent?

$\frac{7}{5}$ and $\frac{42}{30}$

Yes
No