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

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

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

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

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

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

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

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

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 division4m = 52 (the inverse operation of multiplication).4 4 a m = 13 Matthew is 13 years old. Example 2 Four times Peter’s age

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. Communication Prompt

Solve each equation. Show all work and check your solution. 1.9x = = 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. Exit Problems x = 9 k = 28 y = 4 4j = 44; j = 11