Numbers and Operations

Chapter 1

Numbers and Operations

Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Numbers And Operations

1. Uses the language of ratio and rate to describe relationships between two quantities

A ratio expresses the relationship between two numbers through division. It answers the question “how many of one thing are there for each of another?” Ratios can be written in three equivalent ways: as a fraction a/b, with a colon a:b, or with words a to b.

Ratios can be part-to-part, such as the number of boys to the number of girls in a class, or part-to-whole, such as the number of boys to the total number of students. If a class has 8 boys and 12 girls, then the part-to-part ratio is 8:12 = 2:3, and the part-to-whole ratio is 8:20 = 2:5.

Rates are ratios where the two numbers have different units. Examples include miles per gallon, dollars per pound, or words read per minute. A unit rate is the value per one unit. If a car travels 180 miles in 3 hours, the rate is 180 ÷ 3 = 60 miles per hour. If 4 pounds of apples cost $6, the unit rate is 6 ÷ 4 =$1.50 per pound.