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Splash Screen Chapter 6 Algebra: Use Multiplication and Division Click the mouse or press the space bar to continue. Chapter 6 Algebra: Use Multiplication and Division Click the mouse or press the space bar to continue.

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Chapter Menu Lesson 6-1Lesson 6-1Multiplication and Division Expressions Lesson 6-2Lesson 6-2Problem-Solving Strategy: Work Backward Lesson 6-3Lesson 6-3Order of Operations Lesson 6-4Lesson 6-4Algebra: Solve Equations Mentally Lesson 6-5Lesson 6-5Problem-Solving Investigation: Choose a Strategy Lesson 6-6Lesson 6-6Algebra: Find a Rule Lesson 6-7Lesson 6-7Balanced Equations 6 6 Algebra: Use Multiplication and Division

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Lesson 1 Menu Five-Minute Check (over Chapter 5) Main Idea California Standards Example 1: Find the Value of an Expression Example 2: Find the Value of an Expression Example 3: Write an Expression 6-1 Multiplication and Division Expressions

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Lesson 1 MI/Vocab 6-1 Multiplication and Division Expressions I will write and find the value of multiplication and division expressions.

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Lesson 1 Standard 6-1 Multiplication and Division Expressions Standard 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).

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Lesson 1 Ex1 4 × nWrite the expression. 6-1 Multiplication and Division Expressions Jake had 4 boxes of apples. There are 6 apples in each box. Find the value of 4 × n if n = 6.

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Lesson 1 Ex1 4 × 6Replace n with 6. 24Multiply 4 and 6. 6-1 Multiplication and Division Expressions Answer: So, the value of 4 × n is 24. Jake had 24 apples.

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Lesson 1 CYP1 Marian has 5 CD cases. Each CD case has 2 CDs inside. Find the value of 5 × n if n = 2. 6-1 Multiplication and Division Expressions A.7 CDs B.10 CDs C.5 CDs D.2 CDs

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Lesson 1 Ex2 6-1 Multiplication and Division Expressions Find the value of x ÷ (3 × 2) if x = 30. x ÷ (3 × 2)Write the expression. 30 ÷ (3 × 2)Replace x with 30. 30 ÷ 6Find (3 × 2) first. Answer: So, the value of x ÷ (3 × 2) if x = 30 is 5. 5 Next, find 30 ÷ 6.

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Lesson 1 CYP2 6-1 Multiplication and Division Expressions A.9 B.45 C.5 D.1 Find the value of 45 ÷ (x × 1) if x = 5.

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Lesson 1 Ex3 Judy has d dollars to buy bottles of water that cost $2 each. Write an expression for the number of bottles of water she can buy. Answer: So the number of bottles of water Judy can buy is d ÷ 2. Words Variable Expression dollars Let d = dollars. divided by cost dollars d divided by ÷ cost $7 6-1 Multiplication and Division Expressions

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Lesson 1 CYP3 Toby has d dollars to spend on discounted books that cost $3 a piece. Write an expression for the number of books he can buy. A. d ÷ 3 B. d – 3 C. d + 3 D. d × 3 6-1 Multiplication and Division Expressions

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End of Lesson 1

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Lesson 2 Menu Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1: Problem-Solving Strategy 6-2 Problem-Solving Strategy: Work Backward

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Lesson 2 MI/Vocab 6-2 Problem-Solving Strategy: Work Backward I will solve problems by working backward.

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Lesson 2 Standard 1 6-2 Problem-Solving Strategy: Work Backward Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

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Lesson 2 Standard 2 6-2 Problem-Solving Strategy: Work Backward Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

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Lesson 2 Ex1 Currently, there are 25 students in the chess club. Last October, 3 students joined. Two months before that, in August, 8 students joined. How many students were in the club originally? 6-2 Problem-Solving Strategy: Work Backward

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Lesson 2 Ex1 Understand What facts do you know? Currently, there are 25 students in the club. 3 students joined in October. 8 students joined in August. What do you need to find? The number of students that were in the club originally. 6-2 Problem-Solving Strategy: Work Backward

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Lesson 2 Ex1 Plan Work backward to solve the problem. 6-2 Problem-Solving Strategy: Work Backward

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Lesson 2 Ex1 Solve Work backward and use inverse operations. Start with the end result and subtract the students who joined the club. 6-2 Problem-Solving Strategy: Work Backward 22 25 – 3

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Lesson 2 Ex1 Solve Answer: So, there were 14 students in the club originally. 6-2 Problem-Solving Strategy: Work Backward 14 22 – 8

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Lesson 2 Ex1 Check Look back at the problem. A total of 3 + 8 or 11 students joined the club. So, if there were 14 students originally, there would be 14 + 11 or 25 students in the club now. The answer is correct. 6-2 Problem-Solving Strategy: Work Backward

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End of Lesson 2

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Lesson 3 Menu Five-Minute Check (over Lesson 6-2) Main Idea and Vocabulary California Standards Key Concept: Order of Operations Example 1: Use the Order of Operations Example 2: Use the Order of Operations 6-3 Order of Operations

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Lesson 3 MI/Vocab 6-3 Order of Operations I will use the order of operations to find the value of expressions. order of operations

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Lesson 3 Standard 1 6-3 Order of Operations Standard 4AF1.2 Interpret and evaluate mathematical expressions that now use parentheses. Standard 4AF1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

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Lesson 3 Key Concept 1 6-3 Order of Operations

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Lesson 3 Ex1 6-3 Order of Operations 12– 3 ÷ 6 10 Write the expression. Multiply and divide from left to right. 6 ÷ 3 = 2 Add and subtract from left to right. 12 – 2 = 10 Parentheses first. (2 + 4) = 6 12 (4 2) 3–÷ + 12–2 Find the value of 12 – (4 + 2) ÷ 3.

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Lesson 3 CYP1 6-3 Order of Operations A.16 B.1 C.8 D.12 Find the value of 21 ÷ (3 + 4) + 5.

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Lesson 3 Ex2 Follow the order of operations. 6-3 Order of Operations 4x + 3y ÷ 2 = 4 × 7 + 3 × 2 ÷ 2 Replace x with 7 and y with 2. Multiply and divide from left to right. 4 × 7 = 28, 3 × 2 = 6, and 6 ÷ 2 = 3 Add. = 2862+÷ = 3 + = 31 Answer: 31 Find the value of 4x + 3y ÷ 2, when x = 7 and y = 2.

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Lesson 3 CYP2 6-3 Order of Operations A.19 B.11 C.21 D.12 Find the value of 3x – 2y + 12 when x = 5 and y = 3.

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End of Lesson 3

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Lesson 4 Menu Five-Minute Check (over Lesson 6-3) Main Idea California Standards Example 1: Solve Multiplication Equations Example 2: Solve Division Equations Example 3: Write and Solve Equations 6-4 Algebra: Solve Equations Mentally Multiplication and Division Equations

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Lesson 4 MI/Vocab 6-4 Algebra: Solve Equations Mentally I will solve multiplication and division equations mentally.

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Lesson 4 Standard 6-4 Algebra: Solve Equations Mentally Standard 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).

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Lesson 4 Ex1 6-4 Algebra: Solve Equations Mentally The All-Stars Used Car Lot has 8 rows of cars with a total of 32 cars. Solve 8 × c = 32 to find how many cars are in each row.

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Lesson 4 Ex1 6-4 Algebra: Solve Equations Mentally Step 1 Model the equation. One Way: Use Models

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Lesson 4 Ex1 6-4 Algebra: Solve Equations Mentally Step 2 Find the value of c. One Way: Use Models 8 × c = 32 c = 4

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Lesson 4 Ex1 6-4 Algebra: Solve Equations Mentally 8 × c = 32 You know that 8 × 4 = 32.8 × 4 = 32 Answer: So, c = 4. Another Way: Mental Math

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Lesson 4 CYP1 6-4 Algebra: Solve Equations Mentally A.6 rows B.7 rows C.8 rows D.49 rows Kyung has just planted a garden. He has a total of 49 vegetables with 7 vegetables in each row. Solve 7 × v = 49 to find how many rows of vegetables there are.

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Lesson 4 Ex2 16 ÷ s = 8 Answer: So, the value of s is 2. 6-4 Algebra: Solve Equations Mentally 16 ÷ 2 = 8 s = 2You know that 16 ÷ 2 = 8. Solve 16 ÷ s = 8.

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Lesson 4 CYP2 6-4 Algebra: Solve Equations Mentally A.6 B.7 C.8 D.9 Solve 36 ÷ p = 6.

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Lesson 4 Ex3 Six friends went shopping. They each bought the same number of T-shirts. A total of 24 T-shirts were bought. Write and solve an equation to find out how many T-shirts each person bought. Write the equation. 6-4 Algebra: Solve Equations Mentally Words Variable Expression 6 friends bought 24 T-shirts. Let t = the number of T-shirts bought per person. 6 × t = 24

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Lesson 4 Ex3 Solve the equation. 6 × t = 24 Answer: So each person bought 4 T-shirts. 6-4 Algebra: Solve Equations Mentally 6 × 4 = 24 t = 4

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Lesson 4 CYP3 6-4 Algebra: Solve Equations Mentally A.7 golf balls B.8 golf balls C.9 golf balls D.10 golf balls Six friends went to a driving range and hit a total of 54 golf balls. If they all hit the same number of golf balls, how many did each one hit?

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End of Lesson 4

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Lesson 5 Menu Five-Minute Check (over Lesson 6-4) Main Idea California Standards Example 1: Problem-Solving Investigation 6-5 Problem-Solving Investigation: Choose a Strategy

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Lesson 5 MI/Vocab 6-5 Problem-Solving Investigation: Choose a Strategy I will choose the best strategy to solve a problem.

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Lesson 5 Standard 1 6-5 Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

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Lesson 5 Standard 2 6-5 Problem-Solving Investigation: Choose a Strategy 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

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Lesson 5 Ex1 MATT: I take 30-minute guitar lessons two times a week. How many minutes do I have guitar lessons in six weeks? YOUR MISSION: Find how many minutes Matt has guitar lessons in six weeks. 6-5 Problem-Solving Investigation: Choose a Strategy

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Lesson 5 Ex1 Understand 6-5 Problem-Solving Investigation: Choose a Strategy What facts do you know? Each lesson Matt takes is 30 minutes long. He takes lessons two times a week. What do you need to find? Find how many minutes Matt has guitar lessons in six weeks.

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Lesson 5 Ex1 Plan You can use a table to help you solve the problem. 6-5 Problem-Solving Investigation: Choose a Strategy

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Lesson 5 Ex1 Solve Find how many minutes Matt has lessons each week. 6-5 Problem-Solving Investigation: Choose a Strategy 60 30 + 30 lesson 1 lesson 2 minutes per week

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Lesson 5 Ex1 Solve 6-5 Problem-Solving Investigation: Choose a Strategy Find how many minutes Matt has lessons in six weeks. Answer: So, Matt has lessons 360 minutes in six weeks. 60 120180240300360

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Lesson 5 Ex1 Check Look back at the problem. Subtract 60 from 360 six times. The result is 0. So, the answer is correct. 6-5 Problem-Solving Investigation: Choose a Strategy

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End of Lesson 5

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Lesson 6 Menu Five-Minute Check (over Lesson 6-5) Main Idea California Standards Example 1: Find a Multiplication Rule Example 2: Find a Multiplication Rule Example 3: Find a Division Rule Example 4: Find a Division Rule 6-6 Algebra: Find a Rule

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Lesson 6 MI/Vocab 6-6 Algebra: Find a Rule I will find and use a rule to write an equation.

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Lesson 6 Standard 6-6 Algebra: Find a Rule Standard 4AF1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.

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Lesson 6 Ex1 6-6 Algebra: Find a Rule Mike earns $10 when he babysits for 2 hours. He earns $20 when he babysits for 4 hours. If he babysits for 6 hours, he earns $30. Write an equation that describes the money Mike earns. Put the information in a table. Then look for a pattern to describe the rule.

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Lesson 6 Ex1 6-6 Algebra: Find a Rule Pattern:2 × 5 = 10 4 × 5 = 20 6 × 5 = 30 Rule:Multiply by 5. Equation:x × 5 = y

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Lesson 6 Ex1 6-6 Algebra: Find a Rule Answer: The equation x × 5 = y describes the money Mike earns from babysitting.

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Lesson 6 CYP1 6-6 Algebra: Find a Rule A. 8x = y B. x + y = 8 C. 2x + 8 = y D. x × 8 = y Ricardo earns $16 dollars when he mows 2 lawns of grass. He earns $32 when he mows 4 lawns, and $48 when he mows 6 lawns. Write an equation that describes the money Ricardo earns.

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Lesson 6 Ex2 6-6 Algebra: Find a Rule Use the equation x × 5 = y to find how much money Mike earns for babysitting for 8, 9, or 10 hours.

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Lesson 6 Ex2 6-6 Algebra: Find a Rule x × 5 = y 8 × 5 = $40 9 × 5 = $4510 × 5 = $50 40 45 50

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Lesson 6 Ex2 6-6 Algebra: Find a Rule Answer: So, Mike will earn $40, $45, or $50 if he babysits for 8, 9, or 10 hours.

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Lesson 6 CYP2 6-6 Algebra: Find a Rule A.$49, $64 B.$15, $16 C.$56, $64 D.$63, $72 Use the equation x × 8 = y to find how much money Ricardo earns for mowing 7 or 8 lawns.

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Lesson 6 Ex3 The cost of admission into a water park is shown in the table at the right. Write an equation that describes the number pattern. 6-6 Algebra: Find a Rule

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Lesson 6 Ex3 6-6 Algebra: Find a Rule Pattern: 6 ÷ 6 = 1 12 ÷ 6 = 2 18 ÷ 6 = 3 Rule:Divide by 6. Equation:c ÷ 6 = n

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Lesson 6 Ex3 6-6 Algebra: Find a Rule Answer: The equation c ÷ 6 = n describes the cost of admission into the water park.

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Lesson 6 CYP3 6-6 Algebra: Find a Rule A. c ÷ 9 = n B. c + 9 = n C. c + n = 9 D. c – 9 = n The cost of admission into a basketball game is shown in the table below. Write an equation that describes the number pattern.

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Lesson 6 Ex4 6-6 Algebra: Find a Rule Use the equation c ÷ 6 = n to find how many people will be admitted to the park for $24, $30, and $36.

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Lesson 6 Ex4 6-6 Algebra: Find a Rule c ÷ 6 = n 24 ÷ 6 = 4 30 ÷ 6 = 536 ÷ 6 = 6 4 5 6

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Lesson 6 Ex4 6-6 Algebra: Find a Rule Answer: So, $24, $30, and $36 will buy tickets for 4, 5, and 6 people.

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Lesson 6 CYP4 6-6 Algebra: Find a Rule A. 4 people, 5 people B. 5 people, 6 people C. 7 people, 8 people D. 5 people, 7 people Use the equation c ÷ 9 = n to find how many people will be admitted to the basketball game for $45 and $63.

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End of Lesson 6

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Lesson 7 Menu Five-Minute Check (over Lesson 6-6) Main Idea California Standards Example 1: Balanced Equations Example 2: Balanced Equations Example 3: Find Missing Numbers Example 4: Find Missing Numbers 6-7 Balanced Equations

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Lesson 7 MI/Vocab 6-7 Balanced Equations I will balance multiplication and division equations.

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Lesson 7 Standard 6-7 Balanced Equations Standard 4AF2.2 Know and understand that equals multiplied by equals are equal.

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Lesson 7 Ex1 Show that the equality of 6r = 24 does not change when each side of the equation is divided by 6. 6r = 24 6-7 Balanced Equations Write the equation. 6r ÷ 6 = 24 ÷ 6 Divide each side by 6. r = 4 Answer: So, r = 4.

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Lesson 7 Ex1 Check 6-7 Balanced Equations 6r = 24 6 × 4 = 24 24 = 24 Replace r with 4.

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Lesson 7 CYP1 6-7 Balanced Equations A.3y ÷ 3 = 9 ÷ 3; 6 = 6 B.3y ÷ 3 = 9 ÷ 3; 3 = 3 C.3y ÷ 3 = 9; 9 = 9 D.3y = 9 ÷ 3; 3 = 9 Show that the equality of 3y = 9 does not change when each side of the equation is divided by 3.

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Lesson 7 Ex2 6-7 Balanced Equations q ÷ 7 = 4 q ÷ 7 × 7 = 4 × 7 q = 28 Write the equation. Multiply each side by 7. Answer: So, q = 28. Show that the equality of q ÷ 7 = 4 does not change when each side of the equation is multiplied by 7.

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Lesson 7 Ex2 Check 6-7 Balanced Equations q ÷ 7 = 4 28 ÷ 7 = 4 4 = 4 Replace q with 28.

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Lesson 7 CYP2 6-7 Balanced Equations Show that the equality v ÷ 5 = 5 does not change when each side of the equation is multiplied by 5. A. v ÷ 5 × 5 = 5; 10 = 10 B. v ÷ 5 × 5 = 5 × 5; 25 = 25 C. v ÷ 5 = 5; 5 = 5 D. v ÷ 5 × 5 = 5 × 5; 10 = 10

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Lesson 7 Ex3 Write the equation. Each side of the equation must be multiplied by the same number to keep the equation balanced. Answer: So, the missing number is 4. Find the missing number in 5 × 10 × 4 = 50 ×. 6-7 Balanced Equations 5 × 10 × 4 = 50 × You know that 5 × 10 = 50.

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Lesson 7 CYP3 6-7 Balanced Equations A.8 B.5 C.3 D.40 Find the missing number in 8 × 5 × 3 = 40 ×.

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Lesson 7 Ex4 6-7 Balanced Equations Write the equation. You know that 2 × 12 = 24. Each side of the equation must be divided by the same number to keep the equation balanced. Answer: So, the missing number is 4. Find the missing number in 2 × 12 ÷ 4 = 24 ÷. 2 × 12 ÷ 4 = 24 ÷

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Lesson 7 CYP4 6-7 Balanced Equations A.4 B.11 C.44 D.2 Find the missing number in 4 × 11 ÷ 2 = 44 ÷.

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End of Lesson 7

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6 6 Algebra: Use Multiplication and Division 6 6 CR Menu Five-Minute Checks Math Tool Chest Image Bank Multiplication and Division Equations

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6 6 Algebra: Use Multiplication and Division IB Instructions To use the images that are on the following four slides in your own presentation: 1.Exit this presentation. 2.Open a chapter presentation using a full installation of Microsoft ® PowerPoint ® in editing mode and scroll to the Image Bank slides. 3.Select an image, copy it, and paste it into your presentation.

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6 6 Algebra: Use Multiplication and Division IB 1

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6 6 Algebra: Use Multiplication and Division IB 2

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6 6 Algebra: Use Multiplication and Division IB 3

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6 6 Algebra: Use Multiplication and Division IB 4

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6 6 Algebra: Use Multiplication and Division 6 6 5Min Menu Lesson 6-1Lesson 6-1(over Chapter 5) Lesson 6-2Lesson 6-2(over Lesson 6-1) Lesson 6-3Lesson 6-3(over Lesson 6-2) Lesson 6-4Lesson 6-4(over Lesson 6-3) Lesson 6-5Lesson 6-5(over Lesson 6-4) Lesson 6-6Lesson 6-6(over Lesson 6-5) Lesson 6-7Lesson 6-7(over Lesson 6-6)

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6 6 Algebra: Use Multiplication and Division A.composite B.prime C.neither 5Min 1-1 (over Chapter 5) Tell whether 13 is composite, prime, or neither.

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6 6 Algebra: Use Multiplication and Division A.composite B.prime C.neither 5Min 1-2 (over Chapter 5) Tell whether 26 is composite, prime, or neither.

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6 6 Algebra: Use Multiplication and Division 5Min 1-3 (over Chapter 5) A.composite B.prime C.neither Tell whether 37 is composite, prime, or neither.

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6 6 Algebra: Use Multiplication and Division 5Min 1-4 (over Chapter 5) A.composite B.prime C.neither Tell whether 1 is composite, prime, or neither.

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6 6 Algebra: Use Multiplication and Division 5Min 1-5 (over Chapter 5) A.composite B.prime C.neither Tell whether 21 is composite, prime, or neither.

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6 6 Algebra: Use Multiplication and Division A.18 B.14 C.40 D.80 5Min 2-1 (over Lesson 6-1) Find the value of the expression if m = 4. m × 10

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6 6 Algebra: Use Multiplication and Division 5Min 2-2 (over Lesson 6-1) A.1.5 B.6 C.12 D.36 Find the value of the expression if m = 4 and n = 8. 3 × (n ÷ m)

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6 6 Algebra: Use Multiplication and Division 5Min 2-3 (over Lesson 6-1) A.6 B.16 C.24 D.64 Find the value of the expression if m = 4 and n = 8. (12 ÷ m) × n

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6 6 Algebra: Use Multiplication and Division 5Min 2-4 (over Lesson 6-1) A.6 B.16 C.30 D.64 Find the value of the expression if m = 4 and n = 8. (n × m) ÷ 2

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6 6 Algebra: Use Multiplication and Division A.7 bars B.5 bars C.3 bars D.1 bar 5Min 3-1 (over Lesson 6-2) Work backward to solve the problem. Lance had 4 granola bars left from his weekend hike. On Saturday, he ate 2 bars. Before he left for the trip on Friday, his mother added 5 bars to what he had. How many bars did he have to start with?

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6 6 Algebra: Use Multiplication and Division 5Min 4-1 (over Lesson 6-3) A.6 B.11 C.13 D.14 Find the value of the expression. 4 + (5 × 2) – 1

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6 6 Algebra: Use Multiplication and Division 5Min 4-2 (over Lesson 6-3) A.12 B.15 C.24 D.36 Find the value of the expression. 6 + 6 × 3

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6 6 Algebra: Use Multiplication and Division 5Min 4-3 (over Lesson 6-3) A.6 B.7 C.8 D.22 Find the value of the expression. (17 – 3) – (2 × 4)

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6 6 Algebra: Use Multiplication and Division 5Min 4-4 (over Lesson 6-3) A.9 B.10 C.21 D.22 Find the value of the expression. (21 ÷ 3) + 3

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6 6 Algebra: Use Multiplication and Division A.4 B.20 C.5 D.6 5Min 5-1 (over Lesson 6-4) Solve 5 × x = 25 mentally.

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6 6 Algebra: Use Multiplication and Division A.8 B.48 C.49 D.7 5Min 5-2 (over Lesson 6-4) Solve 56 ÷ m = 8 mentally.

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6 6 Algebra: Use Multiplication and Division A.21 B.3 C.24 D.7 5Min 5-3 (over Lesson 6-4) Solve r ÷ 7 = 3 mentally.

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6 6 Algebra: Use Multiplication and Division 5Min 5-4 (over Lesson 6-4) A.3 B.45 C.4 D.36 Solve k × 9 = 36 mentally.

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6 6 Algebra: Use Multiplication and Division 5Min 6-1 (over Lesson 6-5) A.Jacobo will be 12 and his brother will be 6. B.Jacobo will be 8 and his brother will be 4. C.Jacobo will be 7 and his brother will be 3. D.Jacobo will be 10 and his brother will be 6. Use any strategy to solve. Jacobo is 6 years old and his brother is 2 years old. How old will each of them be when Jacobo is twice his brother’s age?

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6 6 Algebra: Use Multiplication and Division A.Multiply by 4; x × 4 = y; 18 B.Add 8; x + 8 = y; 14 C.Multiply by 3; x × 3 = y; 18 D.Multiply by 3; y × 3 = x; 18 5Min 7-1 (over Lesson 6-6) Find a rule and equation that describes the pattern. Then use the equation to find the missing number.

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