## Write a comparison as a rate

The heart of middle school mathematics, and a key part of algebra readiness, is understanding ratios and rates. The overview and lessons below are tools to prepare students, usually in Grades 6 and up, who are ready to learn about these concepts.

## Intro to rates

The lessons below will typically cover two days of instruction. A ratio is a comparison of two numbers or measurements. The numbers or measurements being compared are sometimes called the terms of **write a comparison as a rate** ratio. For example, if a store sells 6 red shirts and 8 green shirts, the ratio of red to green shirts is 6 to 8. A rate is a special ratio in which the two terms are in different units.

This is not a ratio of two like units, such as comparrison. This is a ratio of two unlike units: cents and ounces. But notice that this time, a new unit is created: cents per hour. Rates are used by people every day, such as when they work 40 hours per week or earn interest every year at a bank.

## Write a Rate as a Fraction

When rates are expressed as a quantity of 1, such as 2 feet arte second that is, per 1 second or 5 miles per hour that is, per 1 hourthey can be defined as unit rates.

You can write any rate as a unit rate by reducing the fraction so it has a 1 as the denominator or second term.

As a unit rate example, you can show that the unit rate of comparisson for every 3 buses is 40 students per bus. Rate and unit rate are used to solve many real-world problems. Look at the following problem.

## Rates in the Real World

At that rate, how many hours will she work **write a comparison as a rate** 12 weeks? Removing the units makes the calculation easier to see. However, it is important to remember the units when interpreting the new ratio. When you find equal ratios, it is important to remember that if you multiply or divide one term of a ratio by a number, then you need to multiply or divide the other term by that same number.

## Ratios and Rates

Let's take a look at a problem that involves unit price. How much would 10 pens cost? Your xomparison have no doubt encountered rates and ratios before have they seen a speed limit sign? Prerequisite Skills and Concepts: Students should have a basic understanding of ratios, how to write them, and an ability to simplify a ratio.

Students should also have an ability to work with fractions and **write a comparison as a rate** equivalent fractions. Now that students know how to find a unit rate, they will learn how to find an equivalent ratio using unit rates. Finding equivalent ratios uses the same thought process as finding equivalent fractions. Standard: Use ratio qrite rate reasoning to find equivalent ratios x solve real-world problems 6. Looking for more free math lessons and activities for elementary school students?]