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Core Focus on Introductory Algebra

Learn how to solve equations involving multiplication and division using the equation mat, chips, and variable cubes.

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Core Focus on Introductory Algebra

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  1. Lesson 3.5 Core Focus on Introductory Algebra Solving Multiplication and Division Equations

  2. Warm-Up Solve each equation. Show all work and check your solution. 1. m + 72 = 100 2. 220 = y− 101 3. a− 6.6 = 8.9 4. x + 84 = 233 m = 28 y = 321 a = 15.5 x = 149

  3. Lesson 3.5 Solving Multiplication and Division Equations Solve equations involving multiplication or division.

  4. Explore! Multiplication Equations Step 1 If you do not have an equation mat, draw one like the one seen below on a blank sheet of paper. Step 2 On the equation mat, place two variable cubes on one side. On the other side of the mat, place 6 chips. This represents the equation 2x = 6. Step 3 Divide the chips into two equal groups since there are two variable cubes. How many chips are equal to one variable cube? This is the value of x. Step 4 Clear the mat and place counters on the mat to represent the equation 4x = 8. Draw this on your paper. Step 5 How can you determine how many chips are equal to one variable cube? Step 6 Create a multiplication equation on the mat. Record the algebraic equation on your paper. Step 7 Solve the equation. What does the variable equal? Step 8 Write a few sentences that describe how to solve a multiplication equation using the equation mat, chips and variable cubes.

  5. The Multiplication Property of Equality For any numbers a, b and c: If a = b, then a · c = b · c

  6. The Division Property of Equality For any numbers a, b and c: If a = b, then .

  7. Example 1 The fraction bar is used to show division when solving equations. Solve each equation. Show your work and check your solution. a. b.  

  8. Example 1 Continued… Solve each equation. Show your work and check your solution. c. 11p = 99 d. 12x = 60 11 11a p = 9 a  11(9) = 99a 12 12a x = 5 a  12(5) = 60a

  9. Example 2 Peter is four times older than his son, Matthew. Peter is 52 years old. Write a multiplication equation and solve the equation to determine Matthew’s age. Let m represent Matthew’s age. Write the equation that represents this situation. 4m = 52 Solve the equation by using division 4m = 52 (the inverse operation of multiplication). 4 4a m = 13 Matthew is 13 years old. Peter’s age Four times

  10. Communication Prompt You have learned how to solve four types of equations in this Block (addition, subtraction, multiplication and division). Explain how you are able to tell which operation to use to solve an equation.

  11. Exit Problems Solve each equation. Show all work and check your solution. 1. 9x = 81 2. 7 = 3. 1.5y = 6 4. Ethan is 4 times older than Juan. Ethan is 44 years old. Let j represent Juan’s age. Write and solve a multiplication equation to determine Juan’s age. x = 9 k = 28 y = 4 4j = 44; j = 11

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