Solving Multiplication and Division

EquationsSection 6.2

Objective: Solve one-step multiplication and division

equations

Vocabulary

Coefficient

Division Property of Equality

Multiplication Property of Equality

Notes

You can use the Division Property of Equality to solve multiplication equations.

You can also use the Multiplication Property of Equality to solve division equations.

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

x 3

m = 30

Check. Use the original equation.

m ÷ 3 = 1030 ÷ 3 = 10

10 = 10

Example 2

7b = 105The inverse of multiplying is dividing.

÷ 7 ÷ 7b =1057

1

735

5

350

15

Check

7b = 1057(15) = 105

105 = 105

Using the Division Property of Equality• 1. Solve 20 = 4x. Check your solution.

• 2. Solve -8y = 24. Check your solution.

• 3. Solve -9d = -72. Check your solution.

Using the Division Property of Equality

4. Lelah sent 574 text messages last week. On average, how many messages did she send each day?

5. Antonia earns $6 per hour helping her grandmother. Write and solve an equation to find how many hours she needs to work to earn $48.

Using the Multiplication Property of Equality

Using the Multiplication Property of Equality

Word Problem Practice

1. Raul is solving -6x = 72. Find his mistake and correct it.

Word Problem Practice2. True or False. To solve the equation 5x = 20, you can use the Multiplication Property of Equality. Explain your reasoning.____________________________________________________________________________________________________________________________________

3. A dragonfly can fly a distance of 50 feet at a speed of 25 feet per second. Find the time in seconds. Write the equation in the form d = rt, then solve.____________________________________________________________________________________________________________________________________

Essential Question

• How is the process for solving multiplication and division one-step equations like solving one-step addition and subtraction equations?

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