Ratios

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 can ratios be expressed?

Back

Ratios can be expressed in three ways: as a fraction (e.g., 2/3), with a colon (e.g., 2:3), or in words (e.g., 2 to 3).

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between quantities, even if the numbers are different (e.g., 1:2 is equivalent to 2:4).

Front

If there are 10 girls for every 12 boys, what is the ratio of girls to boys?

Back

The ratio of girls to boys is 10:12, which simplifies to 5:6.

Front

What is the ratio of red marbles to yellow marbles if there are 2 red and 5 yellow?

Back

The ratio of red to yellow marbles is 2:5.

Front

How do you find an unknown quantity in a ratio?

Back

To find an unknown quantity in a ratio, set up a proportion and solve for the missing value using cross-multiplication.

Front

If a recipe calls for 2 cups of flour to 3 cups of sugar, what is the ratio of flour to sugar?

Back

The ratio of flour to sugar is 2:3.

Front

What is the relationship between the ratios 3:5 and 6:10?

Back

The ratios 3:5 and 6:10 are equivalent because 6 is 2 times 3 and 10 is 2 times 5.

Front

If there are 21 cars for every 5 trucks, how many trucks are there if there are 63 cars?

Back

If there are 63 cars, there are 15 trucks (63 cars ÷ 21 cars/truck = 3 trucks; 3 trucks × 5 = 15 trucks).

Front

What is the first step to simplify the ratio 8:12?

Back

The first step to simplify the ratio 8:12 is to find the greatest common divisor (GCD), which is 4. Then divide both numbers by 4 to get 2:3.