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Course 2 Solving Multiplication Equations

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Objectives Review vocabulary Review vocabulary Review solving equations by adding or subtracting Review solving equations by adding or subtracting Solve multiplication equations using Algebra tiles and paper and pencil Solve multiplication equations using Algebra tiles and paper and pencil Solve practical problems Solve practical problems

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Review Use the following to answer the questions: Use the following to answer the questions: 6x + 5 – 3y = 12 6x + 5 – 3y = 12 Is it an equation, expression or an inequality? How do you know? Is it an equation, expression or an inequality? How do you know? Identify the term(s). Identify the term(s). Identify the variable(s). Identify the variable(s). Identify the constant(s). Identify the constant(s). Identify the coefficient(s). Identify the coefficient(s). Equation, it has an equals sign 6x, 5, 3y and 12 x and y 5 and 12 6 and -3

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Review Remember: Equations must be in balance, like a scale. How would you solve this equation? How would you solve this equation? x – 4 = 12 x – 4 = 12 Use the opposite operation to undo the subtraction. Use the opposite operation to undo the subtraction. x – 4 + 4 = 12 + 4 x – 4 + 4 = 12 + 4 x = 16 x = 16

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Let’s look at how to solve an a multiplication equation. Let’s look at how to solve an a multiplication equation.

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Division Property of Equality If you divide each side of an equation by the same nonzero number, the two sides remain equal. If you divide each side of an equation by the same nonzero number, the two sides remain equal.

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Let’s Try It! 1) 2x = -8 1) 2x = -8 What is the coefficient in this equation? What is the coefficient in this equation? What is the opposite (inverse) of multiplying by 2? What is the opposite (inverse) of multiplying by 2? 2 Dividing by 2

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2x = -8 Use the division property of equality: Use the division property of equality: Divide both sides of the equation by 2 Divide both sides of the equation by 2 2x = -8 2x = -8 2 2 2 2 x = -4 x = -4

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2x = -8 Check: 2x = -8 Check: 2x = -8 Replace the variable with the solution: Replace the variable with the solution: 2(-4) = -8 2(-4) = -8 -8 = -8 -8 = -8

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2) -5m = 40 What is the coefficient in this equation? What is the coefficient in this equation? What is the opposite (inverse) of multiplying by -5? What is the opposite (inverse) of multiplying by -5? Divide both sides of the equation by -5? Divide both sides of the equation by -5? -5m = 40 -5m = 40 -5 -5 -5 -5 m = -8 m = -8 -5 Dividing by -5

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-5m = 40 Check -5m = 40 Check -5m = 40 Replace the variable with the solution: Replace the variable with the solution: -5(-8) = 40 -5(-8) = 40 40 = 40 40 = 40

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3) 30 = 6n What is the coefficient in this equation? What is the coefficient in this equation? What is the opposite (inverse) of multiplying by 6? What is the opposite (inverse) of multiplying by 6? Divide both sides of the equation by 6. Divide both sides of the equation by 6. 30 = 6n 30 = 6n 6 6 6 6 5 = n 5 = n 6 Dividing by 6

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30 = 6n Check 30 = 6n Check 30 = 6n Replace the variable with the solution: Replace the variable with the solution: 30 = 6(5) 30 = 6(5) 30 = 30 30 = 30

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4) 1.2x = -4.8 What is the coefficient in this equation? What is the coefficient in this equation? What is the opposite (inverse) of multiplying by 1.2? What is the opposite (inverse) of multiplying by 1.2? Divide both sides of the equation by 1.2. Divide both sides of the equation by 1.2. 1.2x = -4.8 1.2x = -4.8 1.2 1.2 1.2 1.2 x = -4 x = -4 1.2 Dividing by 1.2

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1.2x = -4.8 Check 1.2x = -4.8 Check 1.2x = -4.8 Replace the variable with the solution: Replace the variable with the solution: 1.2(-4) = -4.8 1.2(-4) = -4.8 -4.8 = -4.8 -4.8 = -4.8

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5) -3y = 2 What is the coefficient in this equation? What is the coefficient in this equation? What is the opposite (inverse) of multiplying by -3? What is the opposite (inverse) of multiplying by -3? Divide both sides of the equation by -3. Divide both sides of the equation by -3. -3y = 2 -3y = 2 -3 -3 -3 -3 y = y = Dividing by -3 -3

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-3y = 2 Check -3y = 2 Check -3y = 2 Replace the variable with the solution: Replace the variable with the solution: -3( ) = 2 -3( ) = 2 2 = 2 2 = 2

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Using an Equation to Solve a Problem 1) Sarah earns $5 per hour when she baby-sits. How many hours does she need to work to earn $75? Write an equation: 5h = 75 Solve the equation: 5h = 75 5 5 h = 15 Sarah must work 15 hours to earn $75.00.

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Using an Equation to Solve a Problem. 2) A 125 pound person uses 4.4 calories per minute when walking. How many minutes will it take this person to use 44 calories? 2) A 125 pound person uses 4.4 calories per minute when walking. How many minutes will it take this person to use 44 calories? Write an equation: Write an equation: 4.4m = 44 4.4m = 44 Solve the equation: Solve the equation: 4.4m = 44 4.4m = 44 4.4 4.4 4.4 4.4 m = 10 A 125 pound person must walk for 10 minutes to use 44 calories. A 125 pound person must walk for 10 minutes to use 44 calories.

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