Rates Study Guide

What is a Rate?

A rate is a comparison between two different kinds of quantities. It is a special ratio in which the two terms are in different units. For example, miles per hour, price per pound, or words per minute are all examples of rates.

Calculating Rates

To calculate a rate, you need to divide one quantity by another. For example, to find the rate of speed, you would divide the distance traveled by the time it took to travel that distance. This gives you the speed in miles per hour (mph).

Unit Rate

A unit rate is a rate in which the second term is 1. For example, if a car travels 60 miles in 2 hours, the unit rate would be 30 miles per hour (60 miles divided by 2 hours).

Examples

1. If a car travels 240 miles in 4 hours, what is the rate of speed in miles per hour?
Rate = 240 miles / 4 hours = 60 miles per hour

2. If a store sells 5 pounds of apples for $10, what is the rate per pound?
Rate = $10 / 5 pounds = $2 per pound

Practice Problems

1. A bike travels 15 miles in 1.5 hours. What is the speed of the bike in miles per hour?

2. A printer can print 300 pages in 5 minutes. What is the rate of printing in pages per minute?

Conclusion

Rates are a way of comparing different quantities and are commonly used in everyday situations. Understanding how to calculate and work with rates is an important skill in math and in real life.

◂Math Worksheets and Study Guides Seventh Grade. Introduction to Algebra

Study Guide

Introduction to Algebra

Activity Lesson

Algebraic Expression Cards

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Introduction to Algebra

Worksheet/Answer key

Algebra Riddles

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.