# Unit Rates and Proportional Reasoning

## Lesson Preview

### What You'll Learn

1. To find unit rates
2. To use unit prices

### … And Why

To find speed, as in Example 2

## Finding Unit Rates

A rate is a ratio that compares two quantities measured in different units. Suppose you read 233 words in two minutes. Your reading rate is .

The rate for one unit of a given quantity is the unit rate. To find a unit rate, divide the first quantity by the second quantity. For a reading rate of , the unit rate is 116.5 words per minute.

Calories

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#### Finding a Unit Rate

A box of cereal contains 8 servings and has a total of 36 grams of fat. Find the unit rate of grams of fat per serving.

The unit rate is , or 4.5 grams per serving.

The model below shows the relationships in Example 1.

You can express speed as a unit rate involving a unit of time. Sometimes the time is given in more than one unit, such as minutes and seconds. Convert the time to a single unit, such as seconds, to find the speed.

#### Real-World Problem Solving

SportsIn 2001, Justyna Bak of Poland set a world record for the women's 3,000-m steeplechase. Her time was 9 min 25.31 s. What was her speed in meters per second? Round your answer to the nearest hundredth.

1. Convert the time to a single unit.

d

Her time was 565.31 s.

1. Write the ratio of meters to seconds. Use a calculator to divide.

d

Justyna Bak's speed was 5.31 m/s.

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