Ratios, Rates, and Unit Rates

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 represented?

Back

Ratios can be represented as fractions, using a colon (e.g., 1:3), or using the word 'to' (e.g., 1 to 3).

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' (e.g., miles per hour).

Front

How do you find a unit rate?

Back

To find a unit rate, divide the total quantity by the number of units. For example, if 4 CDs cost $29, the unit rate is $29 ÷ 4 = $7.25 per CD.

Front

What does it mean for ratios to be equivalent?

Back

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

Are the ratios 12/17 and 10/15 equivalent?

Back

No, the ratios 12/17 and 10/15 are not equivalent.

Front

What is a rate?

Back

A rate is a specific kind of ratio that compares two different kinds of quantities, such as speed (miles per hour) or price (cost per item).

Front

How do you determine if two ratios are proportional?

Back

Two ratios are proportional if their cross products are equal. For example, for ratios a/b and c/d, they are proportional if a*d = b*c.

Front

What is the ratio of 5 dogs to 15 cats?

Back

The ratio of 5 dogs to 15 cats is 1:3.

Front

What is the difference between a ratio and a rate?

Back

A ratio compares two quantities of the same kind, while a rate compares two quantities of different kinds.