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Do the ratios form a proportion: word problems

A proportion is a statement that two ratios are equivalent to each other. Two ratios form a proportion if their cross products are equal.

Do these ratios form a proportion?

Tony swims 10 laps in 30 minutes.
Rogert swims 15 laps in 45 minute.

Write the ratios as fractions. $\frac{10}{30}$ and $\frac{15}{45}$

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

 10 × 45 ? = 15 ×30 450 = 450

The cross products are equal, so the ratios form a proportion
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Do these ratios form a proportion?

Tony reads a 120-page book in 4 hours.
Rogert reads a 160-page book in 5 hours.

Write the ratios as fractions. $\frac{120}{4}$ and $\frac{160}{5}$

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

 120 ×5 ? = 150 × 4 600 ≠ 640

The cross products are not equal, so the ratios do not form a proportion.