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Equivalent ratios: word problems

If two ratios have the same value when simplified, then they are called Equivalent Ratios. In other words, two ratios are equivalent if their cross products are equal.

Are these ratios equivalent?
In a cake recipe, 500 grams of butter are mixed with 800 grams of flour.
In a cake recipe, 125 grams of butter are mixed with 200 grams of flour.

Two ratios are equivalent if their cross products are equal.
Write the ratios as fractions.

$\frac{500}{800}$ and $\frac{125}{200}$

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

 500× 200 ? = 800 × 125 100000 = 100000

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

Are these ratios equivalent?
A builder mixes 10 shovels of cement with 25 shovels of sand.
A builder mixes 5 shovels of cement with 15 shovels of sand.

Two ratios are equivalent if their cross products are equal.
Write the ratios as fractions.

$\frac{10}{25}$ and $\frac{5}{15}$

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

 10×15 ? = 5 ×25 150 ≠ 125

The cross products are not equal, so the ratios are not equivalent.