Dividend in the House

Transcription

1 Dividend in the House Dividing with Volume and Surface Area 4 WARM UP Estimate each quotient LEARNING GOALS Fluently divide multi-digit whole numbers and decimals using long division. Solve real-world problems involving volume. Solve real-world problems involving surface area In elementary school, you learned strategies to divide two whole numbers. In this course, you learned how to divide fractions by fractions. How can you use a standard algorithm for dividing whole numbers and decimals to solve problems? LESSON 4: Dividend in the House M1-165

2 Getting Started Plankton are small organisms that drift in the ocean, too weak to swim against the ocean's current. They serve as food for many larger marine animals. Dimensions of a Tank The Think Tank designs and creates customized tanks and aquariums for oceanographers. A team of oceanographers who study the characteristics of plankton requested several tanks that have a volume of 240 cubic feet and bases with various areas, but they didn t give any heights. Provide The Think Tank with tank heights using the information given. 1. B 5 10 square feet 2. B 5 15 square feet 3. B square feet 3 M1-166 TOPIC 3: Decimals and Volume

3 ACTIVITY 4.1 Division of Decimals and Whole Numbers As you demonstrated, if you know the volume of a right rectangular prism and the area of the base you can divide to determine the height. Likewise, if you know the volume and the height of a rectangular prism, you can calculate the area of the base. If the volume of a right rectangular prism is 3.57 cubic feet and the height is 3 feet, what strategy can you use to determine the area of the base? You can use hundredths grids to model dividing decimals. WORKED EXAMPLE Let s consider First, represent Shade 3 hundredths grids to represent 3. Shade 5 columns in a fourth grid to represent 5 tenths. Then shade 7 more squares to represent 7 hundredths. Next, divide the shaded model into 3 equal groups. To do this, divide the 3 hundredths grids into 3 equal groups. Then, divide the 57 hundredths into 3 equal groups. Group 1 Group 2 Group 3 One whole grid and 19 small squares are in each group. So, = Therefore, the area of the base of a rectangular prism with a volume of 3.57 cubic feet and a height of 3 feet is 1.19 square feet. LESSON 4: Dividend in the House M1-167

4 WORKED EXAMPLE You can also use a standard algorithm to divide tenths divided into 3 equal groups is 1 tenth in each group with 2 tenths left over. 3 ones divided into 3 equal groups is 1 one in each group with 0 ones left over. divisor tenths and 7 hundredths is 27 hundredths. 27 hundredths divided into 3 equal groups is 9 hundredths in each group with 0 hundredths left over. quotient dividend 1. Compare the two worked examples. a. What is the area of the base of the right rectangular prism? An algorithm is a step-by-step procedure for completing a calculation. A standard algorithm is a specific and commonly accepted algorithm. b. Describe how the hundredths grid model represents different parts of the standard algorithm. c. Why does the standard algorithm show subtracting 3 from the 3 ones in the dividend? M1-168 TOPIC 3: Decimals and Volume

5 d. What does the 05 represent in the standard algorithm? e. What does represent in the standard algorithm? Use the hundredths grid model to help you explain. 2. The volume of a right rectangular prism is 26,112 cubic feet and its base has an area of 256 square feet. What is the height? Examine each solution. What did Dustin do incorrectly? Morgan I used my strategy from earlier )26, The height of the right rectangular prism is 102 feet. Dustin The height of the prism should be 12 feet )26, The area of the base of the rectangular prism is 1.19 square feet. Calculate the width of each rectangular prism with the given length. a. Length 5 2 feet b. Length 5 3 feet c. Length 5 4 feet LESSON 4: Dividend in the House M1-169

6 ACTIVITY 4.2 Dividing Decimals You have seen how to divide decimals by whole numbers. Let s think about how to divide decimals by decimals. 1. Look at these division problems. 7c }} 56 70c }}} c }}} c }}}} 56,000 a. How are the divisors and dividends in the last three problems related to the first problem? b. Calculate all four quotients. What do you notice about them? c. What happens to the quotient when the dividend and divisor are multiplied by the same number? Remember the definition of division: a 4 b 5 a b. Therefore, you can use what you already know about equivalent fractions to determine which expressions have the same quotient as Which of the division expressions shown have the same quotient as ? How do you know? a c b d M1-170 TOPIC 3: Decimals and Volume

7 Let s investigate an algorithm for dividing a decimal by a decimal. You already know how to divide a decimal by a whole number. You also know that if you multiply or divide both the dividend and the divisor by the same number, the quotient remains the same. WORKED EXAMPLE The diagram shows The first step is to rewrite the division sentence so the divisor is a whole number. Multiply both the divisor and dividend by 10. This changes the value of both numbers. 77 divided by 35 is 2 with 7 left over, because = tenths divided by 35 is 2 tenths with 0 left over. 2? 2 3? 5? 7? 7? Place the decimal point in the quotient Examine the worked example. a. Explain how the worked example shows that LESSON 4: Dividend in the House M1-171

8 NOTES b. Why does the diagram show subtracting 70 from the 77 in the dividend? c. What does represent in the diagram? 4. Rewrite each division sentence so the divisor is a whole number. Then calculate the quotient using long division. a b c M1-172 TOPIC 3: Decimals and Volume

9 ACTIVITY 4.3 Problem Solving Using Volume and Surface Area Let s apply what you have learned about decimal operations to solve problems with volume and surface area. 1. The surface area for a cube is given. Calculate the area of each face of the cube. Be sure to estimate before you calculate! a square inches b. 768 square feet c square centimeters 2. Marjorie uses a loaf pan to make cornbread. The pan is 8.5 inches long, 4.5 inches wide, and 2.5 inches deep. a. The pan has a volume of approximately 6.6 cups. What is the approximate volume of each cup in cubic inches? Estimate and then calculate your answer. Show your work. b. The cornbread Marjorie makes fills only half the depth of the loaf pan. How much cornbread does Marjorie make? Give your answer in cups and cubic inches. LESSON 4: Dividend in the House M1-173

10 NOTES TALK the TALK A Short Long Division Activity Use the standard algorithm to determine each quotient For each division statement given, write two division statements that have the same quotient M1-174 TOPIC 3: Decimals and Volume

11 Assignment Write Describe what is meant by the operation of division. Remember In a division sentence, if you multiply the dividend and the divisor by the same number, the quotient remains the same = = = Practice Estimate each quotient. Then calculate the quotient using long division. Round to the nearest hundredth Stretch The volume of the trapezoidal prism is cubic feet. Determine the height of the trapezoid base. 4.1 ft? ft 25.2 ft 10 ft Review 1. Mary Alice has decided to give her best friend a candle for her birthday. To wrap the candle, she spends $2.50 on a rectangular sheet of wrapping paper that is 24 inches by 19.5 inches. How many square inches are in one rectangular sheet of wrapping paper? 2. Calculate the surface area of a Rubik s Cube that has a width of 57 millimeters. 3. Determine the area of a triangle that has a height of 4 feet and a base of feet. 4. Determine the quotient Determine the product of each. a b LESSON 4: Dividend in the House M1-175

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