CC Course 1
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· Chapter 7
o 7 Opening
o 7.1.1
o 7.1.2
o 7.1.3
o 7.2.1
o 7.2.2
o 7.2.3
o 7.2.4
o 7.3.1
o 7.3.2
o 7.3.3
o 7.3.4
o 7 Closure
· Chapter 8
· Chapter 9
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· Lección (ESP)
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· This lesson will bring you more division strategies! You will continue your work with dividing fractions to include a new strategy for dividing by fractions. You will also extend your knowledge to division of decimals.
· 7-57.Donald and Ahmad were intrigued by homework problem 7-53 and decided to investigate other pairs of numbers that multiply together to get 1.
·
1. They wrote the following number puzzles. Find the missing number in each of their puzzles and then show how you can find it using division. Note that two numbers whose product is 1 are called multiplicative inverses, also known as reciprocals.
1. 6 · ___ = 1
2. 4 · ___ = 1
3.
2. “Wow!”Donald said, “We can just flip the fraction over to find its multiplicative inverse.” Why does this make sense? Work with your team to explain why any fraction multiplied by the “flipped fraction” (reciprocal) must be equal to 1. Use the fractions below to show your thinking.
1.
2.
3.
· 7-58. Malik and Cheryl were working on the division problem . Malik said, “Since a fraction can mean division, doesn’t that mean that I can write this?”
· He wrote:.
o Cheryl answered,“That's ugly, Malik. It's a super fraction.”
o Malik responded,“Yeah, but then I can use a Giant One!”
· Then he wrote
1. Copy Malik’s expression on your paper and simplify it.
2. Why did Malik choose to use 4s inside his Giant One? What would have happened if he had chosen a different number? Discuss this with your team andbe ready to explain your ideas.
· 7-59. Cheryl was thinking more about Malik’s idea of using a Giant One to help divide and realized it could be used with two fractions. She used the problemto demonstrate her idea, doing the work shown at right.
·
· Cheryl said, “Can we use a Giant One like you did? This time, let’s choose a number to use in the Giant One that will make the denominator of our answer equal to 1.”
1. What number could Cheryl use in her Giant One? In other words, what number multiplied bywill give the answer 1? What is that number called?
2. Copy and complete Cheryl’s calculation. Cheryl called a Giant One made by two fractions a Super Giant One.
3. Show how to writeCheryl’s way and then solve it using a Super Giant One.
· 7-60. Simplify each of the following expressions using a Super Giant One likeCheryl did in problem 7-59.
1.
2.
3.
· 7-61.Anna wants to find the quotient of 0.006 ÷0.25. (A quotient is the answer to a division problem.) However, Anna is not sure how to divide decimals. She decided to rewrite the numbers as fractions.
1. With your team, rewrite 0.006 ÷ 0.25using fractions. Use what you know about dividing fractions to find an answer that is one fraction.
2. “Hmm,”said Anna,“Since the original problem was written with decimals, Ishould probably write my answer as a decimal.” Convert your answer from part(a) to a decimal.
3. Find the quotient 1.035 ÷ 0.015.
· 7-62. Elsha wants to divide 0.07 ÷ 0.004 and thinks she sees a shortcut. “Can I just divide 7 ÷ 4 ?”, she wonders.
1. What do you think? Will Elsha's shortcut work? Discuss this with your team and be prepared to explain why or why not.
2. Determine the answer to 0.07 ÷ 0.004, and show how you found your answer.
· 7-63. LEARNING LOG
· In your Learning Log, explain how to decide what fraction to use in a Super Giant One to eliminate one of the fractions in a division problem. If you need help getting started, review the information in the Math Notes box below. Title this entry “Using a Super Giant One” and label it with today’s date.
·
Multiplicative Inverses and Reciprocals
Two numbers with a product of 1 are called multiplicative inverses.
In general and , where neither a nor b equals zero.Notethat is the reciprocal of a and is the reciprocal of . Note that 0 has no reciprocal.
· 7-64. Without using a calculator, find the following quotients. Homework Help ✎
1.
2. 8.06 ÷ 2.48
3.
· 7-65.Find the multiplicate inverse of each of the following numbers. Refer to the Math Notes box in this lesson for help. Homework Help ✎
1.
2.
3. 1.5
4. 0.25
· 7-66. A Giant One lets you change a decimal division problem into a whole-number division problem. Copy the example below and complete the other problems in the same way. Homework Help ✎
·
Decimal Division Problem / Multiply by Giant One / Whole Number Division Problem / AnswerExample / / / / 10
8.2 ÷ 0.4 /
0.02 ÷ 0.005
10.05 ÷ 0.25
·
· 7-67. This problem is a checkpoint for mutliplying fractions and decimals. It will be referred to as Checkpoint 7A.
Multiply each pair of fractions or each pair of decimals. Simplify if possible.Homework Help ✎
1.
2.
3.
4.
5. 2.71 · 4.5
6. 0.35 · 0.0007
· Check your answers by referring to theCheckpoint 7A materials.
· Ideally, at this point you are comfortable working with these types of problems and can solve them correctly. If you feel that youneed more confidence when solving these types of problems, then review theCheckpoint 7Amaterials and try the practice problems provided. From this point on, you will be expected to do problems like these correctly and with confidence.
· 7-68. The graph at right displays gas mileage for a new car. 7-68 HW eTool (Desmos).Homework Help ✎
1. Use the graph to predict the number of miles the car could travel with three gallons ofgas.
2. Use the graph to predict the number of miles the car could travel with five gallons ofgas.
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