Ratios and 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 write a ratio?

Back

Ratios can be written in three ways: using a colon (e.g., 3:4), as a fraction (e.g., 3/4), or in words (e.g., '3 to 4').

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between numbers, which can be determined by cross-multiplying.

Front

What is the cross product of two ratios?

Back

The cross product of two ratios a:b and c:d is the product of the outer terms (a*d) and the inner terms (b*c). If a*d = b*c, the ratios are equivalent.

Front

If the ratio of basketballs to total balls is 4 to 16, how many total balls are there?

Back

There are 16 total balls (4 basketballs + 7 soccer balls + 5 volleyballs = 16).

Front

How do you find the price per pound if a 10lb pack costs $15?

Back

To find the price per pound, divide the total cost by the weight: $15 ÷ 10 lbs = $1.50 per pound.

Front

What is the ratio of 12 to 32 in simplest form?

Back

The simplest form of the ratio 12 to 32 is 3 to 8.

Front

How can you determine if two ratios are equivalent using cross products?

Back

To determine if two ratios a:b and c:d are equivalent, check if a*d = b*c.

Front

What is the ratio of 4 basketballs to 7 soccer balls?

Back

The ratio of basketballs to soccer balls is 4 to 7.

Front

If a recipe calls for a ratio of 2:3 for sugar to flour, how much sugar is needed for 6 cups of flour?

Back

If the ratio is 2:3, for every 3 parts of flour, there are 2 parts of sugar. For 6 cups of flour, you need 4 cups of sugar.