Solving Multiplication and Division Equations

Solving Multiplication and Division Equations

When solving addition and subtraction equations, there are two ideas that need to be involved...

• 1. There needs to be an inverse relationship.

• 2. Property of equality

Inverse Relationship

• Multiplication undergoes division.

• Division undergoes multiplication.

Property of Equality

The same value can be multiplied or divided from both sides of an equation, and equality is maintained.

How can you get the variable alone in the division equation?

x (2) = 40

2x = 40

• Divide by 2 is the inverse of multiplying by 2.

• SOLVE: 2x = 40

• SOLVE:  $2x\ \div2=40\div2$  --> Dividing by 2 will undo multiplying by 2. That will leave x alone.

• SOLVE:  $x\ =\ 40\div2$  

• SOLVE: x = 20

Checking Our Work:

Equation: 2x = 40

• To check, substitute 20 for x.

• 2x = 40

• 2 (20) = 40

• 40 = 40 --> It checks

How can you get the variable alone in the division equation?

 $x\div2\ =\ 40$  

 $x\div2\ =\ 40$  

• Multiply by 2 is the inverse of dividing by 2. 

• SOLVE:  $x\div2\ =\ 40$  

• SOLVE:  $x\div2\ \left(2\right)\ =\ 40\ \left(2\right)$  --> Multiplying by 2 will undo dividing by 2. That will leave x alone.

• SOLVE: x = 40 (2)

• SOLVE: x = 80

Checking Our Work:
Equation:

 $x\div2\ =\ 40$  

• To check, substitute 80 for x. 

•  $x\div2\ =\ 40$  

•  $80\div2\ =\ 40$  

• 40 = 40 --> It checks

Now It Is Your Turn!

Remember to use the inverse relationship and the property of equality.

Fill in the Blanks

Explain how to get the variable alone in the equation.

18x = 36

Fill in the Blanks

Explain how to get the variable alone in the equation.

 $x\div3\ =10$  

Fill in the Blanks

Solve the equation.

2t = 12

Fill in the Blanks

Solve the equation.

 $r\div5\ =\ 22$  

Fill in the Blanks

Solve the equation.

99 = 3x

Poll

How do you feel on evaluating equations?

• Great!

• So-So.

• Confused?