5.2: Ratios and Equivalence

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a to b' or a:b.

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same fraction.

Front

How do you find an equivalent ratio?

Back

To find an equivalent ratio, you can multiply or divide both terms of the ratio by the same non-zero number.

Front

What is the ratio of 6 to 5 expressed in simplest form?

Back

The ratio 6:5 is already in simplest form.

Front

If the ratio of boys to girls in a class is 3:4, how many boys are there if there are 28 students in total?

Back

There are 12 boys. (3 parts boys out of 7 total parts: 3/7 * 28 = 12)

Front

What is the equivalent ratio of 5:4 when both terms are multiplied by 5?

Back

The equivalent ratio is 25:20.

Front

If you have a ratio of 12:20, what is its simplest form?

Back

The simplest form of 12:20 is 3:5.

Front

How do you write the ratio of 4 nickels to a total of 12 coins?

Back

The ratio is written as 4:12.

Front

What is the relationship between the ratios 3:4 and 6:8?

Back

The ratios 3:4 and 6:8 are equivalent because both can be simplified to the same fraction.

Front

If a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, how much sugar is needed for 4 cups of flour?

Back

You would need 6 cups of sugar. (The ratio 2:3 means for every 2 cups of flour, 3 cups of sugar are needed.)