Ratios, Rates and Unit Rates

Honors Math – Grade 7

Problem of the Day 1

The distance from one base to the next on a softball diamond is 55 feet. The distance from one base to the next on a baseball diamond is 90 ft. Write a ratio that compares base-to-base distances on a softball diamond with base-to-base distances on a baseball diamond.

KEY CONCEPT Ratio

A ratio is a comparison of two quantities, a and b, by divisionwhere b is not equal to 0. These quantities are called terms of the ratio. A ratio can be written in three different forms.

Word Form Ratio Form Fraction Form

KEY CONCEPT Rate

A rate is a ratio that compares two unlike quantities. Toexpress a rate in simplest form, find the unit rate.

KEY CONCEPT Unit Rate

A unit rate is a rate in which the second term, or denominatoris 1.

gal

mi

14

350

Get Ready for the Lesson

To express her rate of energy in simplest form, find the unit rate.

Tina volunteered to take part in a fitness program. In one treadmill test, she burned 96 calories in 12 minutes. How can you express her rate of energy use in simplest form?

min12

96Cal

Tina burned energy at a rate of 8 Calories per minute.

KEY CONCEPT Equal Rates

To find equal rates, find equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero number. Think equivalent fractions.

Method 1 – Multiply both terms by the same nonzero number.

Method 2 – Divide both terms by the same nonzero number.

Find three equal rates.

sec4

30 ft

games

spo

6

int114

Find three equal rates.

h

mi

4

232

people

cups

6212

Find the unit rate.

serv

oz

25

150L

km

14

7

cards12

40.59$

lb4195.0$

According to the table below, which runner burned Calories at the slowest rate?

Which is the better buy, a quart of sports drink for $1.39 or a gallon for $6?

KEY CONCEPT Unit Price

A unit price is a unit rate for an item of purchase.