Solving Multiplication and Division Equations November 19/20th 2012 7.EE.3, 7.EE. 4

Procedure Isolate the variable by performing the inverse operation on the number that is attached to the variable. The inverse of multiplication is division. The inverse of division is multiplication. Use the “Golden Rule.” Perform the same operation on the other side of the equal sign.

Example m ÷ 3 = 10 The inverse of division is multiplication. x 3 x 3 Repeat the operation on the other side. 30 m =

Check. Use the original equation. m ÷ 3 = 10 30 ÷ 3 = 10 10 = 10

Example 2 The inverse of multiplying is dividing. 7b = 105 ÷ 7 ÷ 7 1 5 105 7 b = 15 7 3 5 35

Check 7b = 105 7(15) = 105 105 = 105

Practice Problems 2x = 18 (9) 10x = 70 (7) x/2 = 100 (200) x/3.5 = 12 (42) (5) 7

Real World Problem Solving Wages Suppose you work part-time at the Plymouth Library. You earn $152 for 19 hours of work. What is your hourly wage? Write and solve an algebraic equation to solve this problem. 8

Real World Problem Solving Relate: Define: Write: Number of hours worked times wage equals total earnings. Let w = wage. 19 w = 152 9

Real World Problem Solving 19 19 w = 8 Your hourly wage is $8. 10

Now you try! Car Repair Your bill for car repair is $321.00. One third of the bill is for labor. Write and solve an equation to solve for the cost of labor. 11

Now you try! Relate: Define: Write: The repair bill divided by three equals the cost of labor. Let c = cost of labor 321 = c 3 12

Now you try! 321 = c 3 c = 107 The cost of labor is $107.00