Introduction to Ratios and Proportions Flashcard

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, expressed as 'a:b = c:d'.

Front

How do you solve for a missing value in a proportion?

Back

Cross-multiply the ratios and solve for the unknown value. For example, in the proportion 8:19 = 14:n, you would calculate 8n = 14 * 19.

Front

What does it mean for two ratios to form a proportion?

Back

Two ratios form a proportion if their cross products are equal.

Front

If a:b = 3:4 and b:c = 5:6, how do you find a:c?

Back

To find a:c, multiply the ratios: a:c = (3/4) * (5/6) = 3:6.

Front

What is the value of x in the ratio 15:x if 5:7 is a proportion?

Back

To find x, set up the proportion: 5/7 = 15/x, then cross-multiply to get 5x = 105, so x = 21.

Front

How can you express a ratio in different forms?

Back

Ratios can be expressed as fractions, decimals, or in words (e.g., 5:11, 5/11, or '5 to 11').

Front

What is the ratio of pennies to coins if there are 5 pennies and 11 coins?

Back

The ratio of pennies to coins is 5:11.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be represented as fractions, where the first quantity is the numerator and the second is the denominator.

Front

How do you determine if two ratios are equivalent?

Back

Two ratios are equivalent if they simplify to the same fraction or if their cross products are equal.