Unit Rates and Ratios study guide

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if you travel 60 miles in 2 hours, the unit rate is 30 miles per hour.

Front

How do you simplify a ratio?

Back

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

Front

What is the formula for setting up a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be set up as a/b = c/d, where a, b, c, and d are numbers.

Front

If 22 minutes is needed for 6 people, how do you find the time for 17 people?

Back

Set up the proportion: 22 minutes/6 people = X minutes/17 people. Cross-multiply and solve for X.

Front

What does the slope of a graph represent in a rate context?

Back

The slope represents the rate of change, showing how much one quantity changes in relation to another. For example, in a graph of earnings over time, the slope indicates how much money is earned per hour.

Front

What is a ratio?

Back

A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, the ratio of 4 red apples to 3 green apples is written as 4:3.

Front

How do you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first term as the numerator and the second term as the denominator. For example, the ratio 5:2 can be written as the fraction 5/2.

Front

What is the greatest common divisor (GCD)?

Back

The GCD is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 8 and 12 is 4.

Front

How do you find a unit price?

Back

To find a unit price, divide the total price by the number of units. For example, if 5 apples cost $3, the unit price is $3/5 = $0.60 per apple.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal. For example, if 1/2 = 2/4, then 1:2 is proportional to 2:4.