7S: Ratios, Rates, 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 express a ratio?

Back

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

Front

What is a rate?

Back

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

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve a proportion?

Back

To solve a proportion, you can use cross-multiplication: if a/b = c/d, then a*d = b*c.

Front

If a car travels 280 miles in 7 hours, what is the rate of travel in miles per hour?

Back

The rate is 40 miles per hour (280 miles ÷ 7 hours).

Front

What is the formula for finding the unit rate?

Back

The unit rate is found by dividing the quantity by the number of units, expressed as quantity per 1 unit.

Front

If you travel 150 miles on 5 gallons of gas, how many miles do you travel per gallon?

Back

You travel 30 miles per gallon (150 miles ÷ 5 gallons).

Front

What is the relationship between distance, rate, and time?

Back

The relationship is expressed as: Distance = Rate × Time.

Front

What is the ratio of dogs to all pets if there are 2 dogs, 4 cats, and 5 hamsters?

Back

The ratio of dogs to all pets is 2:11.