Ratios/Rates/Unit Rates

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 in the form 'a:b'.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, to simplify 35:14, divide both by 7 to get 5:2.

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 'a per 1 b'. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find the price per item?

Back

To find the price per item, divide the total cost by the number of items. For example, if 4 tickets cost $252, the price per ticket is $252 ÷ 4 = $63.

Front

What is the difference between part-to-part and part-to-whole ratios?

Back

Part-to-part ratios compare two parts of a whole (e.g., boys to girls), while part-to-whole ratios compare one part to the total (e.g., boys to total students).

Front

If a class has a ratio of boys to girls of 15:12, how many boys are there if there are 12 girls?

Back

To find the number of boys, set up a proportion: 15/12 = x/12. Solving gives x = 15 boys.

Front

What is a rate?

Back

A rate is a specific kind of ratio that compares two different units, such as miles per hour or price per item.

Front

How do you determine which option is a better deal?

Back

To determine the better deal, calculate the unit rate for each option and compare them. The option with the lower unit rate is the better deal.

Front

What is the ratio of wins to losses if a team has won 11 games and lost 1?

Back

The ratio of wins to losses is 11:1.

Front

What does it mean to express a ratio in simplest form?

Back

Expressing a ratio in simplest form means reducing it to its lowest terms, where the two numbers have no common factors other than 1.