4.5 use equivalent ratios

Front

What is an equivalent ratio?

Back

An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers are different. For example, the ratios 1:2 and 2:4 are equivalent.

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. For example, to find an equivalent ratio of 3:4, you can multiply both terms by 2 to get 6:8.

Front

If the ratio of apples to oranges is 2:3, what is the equivalent ratio if there are 8 apples?

Back

The equivalent ratio is 8:12, because if you multiply both terms of the ratio 2:3 by 4, you get 8:12.

Front

What is the purpose of using equivalent ratios?

Back

Equivalent ratios are used to compare quantities and solve problems involving proportions, such as scaling recipes or determining distances.

Front

If a recipe calls for 4 cups of flour and 6 cups of sugar, what is the equivalent ratio of flour to sugar?

Back

The equivalent ratio of flour to sugar is 2:3, which can be found by dividing both terms by 2.

Front

How can you use equivalent ratios to solve for an unknown value?

Back

You can set up a proportion using equivalent ratios and cross-multiply to solve for the unknown value.

Front

If 5 pencils cost $2, how much do 15 pencils cost using equivalent ratios?

Back

Using equivalent ratios, 5 pencils to $2 is equivalent to 15 pencils to $6.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, 1/2 = 2/4 is a proportion.

Front

If the ratio of boys to girls in a class is 3:4 and there are 12 boys, how many girls are there?

Back

There are 16 girls, because the equivalent ratio is 3:4, and if you multiply 3 by 4, you get 12 boys, which means 4 must be multiplied by 4 to get 16 girls.

Front

What is the first step in solving a problem involving equivalent ratios?

Back

The first step is to identify the known ratios and the unknown value you need to find.