## Presentation on theme: "Chapter 7 Measurement © 2010 Pearson Education, Inc. All rights reserved."— Presentation transcript:

7.1 Problem Solving with U.S. Customary Measurements Objectives Slide 7.1- 2 1. Learn the basic U.S. customary measurement units. 2. Convert among measurement units using multiplication or division. 3. Convert among measurement units using unit fractions. 4. Solve application problems using U.S. customary measurement units. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Slide 7.1- 3 In the United States, we still use the U.S. customary measurement units for many everyday activities. Examples are inches, feet, quarts, ounces, and pounds. However, science, medicine, sports, and manufacturing use the metric system (meters, liters, and grams). Copyright © 2010 Pearson Education, Inc. All rights reserved.

Memorize the U.S. customary measurement conversions shown on the previous slide. Then answer these questions. Parallel Example 1 Knowing U.S. Customary Measurement Units Slide 7.1- 5 a. 3 ft = ________ yd b. 1 gal = ________ qt c. 1 hr = ________ min d. 16 oz = ________ lb 1 4 60 1 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Slide 7.1- 6 Copyright © 2010 Pearson Education, Inc. All rights reserved. Converting among Measurement Units 1. Multiply when converting from a larger unit to a smaller unit. 2. Divide when converting from a smaller unit to a larger unit.

Convert each measurement. Parallel Example 2 Converting from One Unit of Measure to Another Slide 7.1- 7 a. 9 ft to inches. larger unit to a smaller unit  multiply Recall, 1 ft = 12 in. 9 ft = 9 12 = 108 in. b. 6 lb to ounces. 1 2 Recall, 1 lb = 16 oz. 6 lb = 6 16 = 104 oz 1 2 1 2 larger unit to a smaller unit  multiply

Convert each measurement. Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 2 Converting from One Unit of Measure to Another Slide 7.1- 8 c. 24 qt to gallons. smaller unit to a larger unit  divide Recall, 4 qt = 1 gal. 24 qt = 4 24 = 6 gal d. 10 min to hours.Recall, 60 min = 1hr. 10 min = 10 60 = 10 ÷ 10 60 ÷ 10 1 6 = hr smaller unit to a larger unit  divide

If you have trouble deciding whether to multiply or divide when converting measurements, use unit fractions to solve the problem. A unit fraction is equivalent to 1. 1 1 Slide 7.1- 9 Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Choosing a Unit Fraction The numerator should use the measurement unit you want in the answer. The denominator should use the measurement unit you want to change.

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 3 Using Unit Fractions with Length Measurements Slide 7.1- 10 Convert 84 in. to feet.  Unit for your answer is feet. Recall, 1 ft = 12 in.  Unit being changed is inches. 1 ft 12 in. 1 ft 12 in. 84 in. = 1 7 1 Divide out inches. 7 1 ft 1 = 7 ft = 84 in. 1 ft 12 in. These units should match.

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 4 Using Unit Fractions with Capacity and Weight Measurements Slide 7.1- 11 a. Convert 7 pints to quarts  Unit for your answer is quarts.  Unit being changed is pints. 1 qt 2 pt 1 qt 2 pt 7 pt = 1 Divide out pints. 7 2 == 7 pt 1 qt 2 pt These units should match. Write as mixed number.

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 4 continued Using Unit Fractions with Capacity and Weight Measurements Slide 7.1- 12 b. Convert to quarts Divide out gallons. Write as an improper fraction. 1 2

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 4 Using Unit Fractions with Capacity and Weight Measurements Slide 7.1- 13 c. Convert 44 oz to pounds Divide out ounces. 4 11

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 5 Using Several Unit Fractions Slide 7.1- 14 a. Convert 81 in. to yards. 1 ft 12 in. 1 yd 3 ft Use the unit fractions:,.

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 5 Using Several Unit Fractions Slide 7.1- 15 b. Convert 3 days to seconds. 60 min 1 hr 24 hr 1 day 3 days 1 60 sec 1 min = 259,200 seconds

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Six Steps to Solving Application Problems (Review) Step 1 Read the problem carefully. Step 2 Work out a plan. Step 3 Estimate a reasonable answer. Step 4 Solve the problem. Step 5 State your answer. Step 6 Check your work. Slide 7.1- 16

A local grocery store has an 18 oz jar of peanut butter on sale for \$1.75. What is the cost per pound, to the nearest cent? Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 6 Solving U.S. Customary Measurement Applications Slide 7.1- 17 Step 1 Read the problem. The problem asks for the cost per pound of peanut butter. Step 2 Work out a plan. The weight of peanut butter is given in ounces but the answer must be cost per pound. Convert ounces to pounds. The word per indicates division. You need to divide the cost by the number of pounds. Step 3 Estimate a reasonable answer. To estimate, round \$1.75 to \$2. Then, there are 16 oz in a pound, so 18 oz are a little more than 1 pound. So, \$2 ÷ 1 = \$2 per pound as our estimate.

A local grocery store has an 18 oz jar of peanut butter on sale for \$1.75. What is the cost per pound, to the nearest cent? Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 6 continued Solving U.S. Customary Measurement Applications Slide 7.1- 18 Step 4 Solve the problem. Use a unit fraction to convert 18 oz to pounds. 18 oz1 lb 16 oz 1 == 9 8 lb 1.125 lb 9 \$1.75 pound Cost per = 1.555 ≈ 1.56 (rounded) Then divide to find the cost per pound. 8

A local grocery store has an 18 oz jar of peanut butter on sale for \$1.75. What is the cost per pound, to the nearest cent? Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Parallel Example 6 continued Solving U.S. Customary Measurement Applications Slide 7.1- 19 Step 5 State the answer. The peanut butter costs \$1.56 per pound (to the nearest cent). Step 6 Check your work. The exact cost of \$1.56 is close to our estimate of \$2.