Ratios, Unit Rates, Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, showing how many times one value contains or is contained within the other.

Front

How do you find the unit rate?

Back

To find the unit rate, divide the total amount by the number of units. For example, if you earn $60 for 8 hours of work, the unit rate is $60 ÷ 8 = $7.50 per hour.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How can you express the ratio of dimes to total coins if you have 3 pennies, 4 nickels, and 5 dimes?

Back

The total number of coins is 3 + 4 + 5 = 12. The ratio of dimes to total coins is 5:12.

Front

What does it mean to calculate equivalent ratios?

Back

Calculating equivalent ratios means finding different ratios that represent the same relationship. You can do this by multiplying or dividing both terms of a ratio by the same number.

Front

If you have a ratio of 2:3, what is an equivalent ratio?

Back

An equivalent ratio could be 4:6, obtained by multiplying both terms by 2.

Front

What is the unit rate of $75 for 5 dinners?

Back

The unit rate is $75 ÷ 5 = $15 per dinner.

Front

How do you solve for k in the proportion 3/k = 5/15?

Back

Cross-multiply to get 3 * 15 = 5 * k, which simplifies to k = 9.

Front

What is the first step in solving a proportion?

Back

The first step is to cross-multiply the two ratios.

Front

If a recipe calls for a ratio of 1:4 of sugar to flour, how much sugar is needed for 2 cups of flour?

Back

If the ratio is 1:4, then for 2 cups of flour, you need 0.5 cups of sugar (1/4 of 2 cups).