1-4 Solving Multiplication and Division Equations

Pre-Algebra

Learn to solve equations using multiplication and division.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Addition and subtraction are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Multiplication and division are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

You can solve a multiplication equation using the Division Property of Equality.

You can divide both sides of an equation by the same nonzero number, and the equation will still be true.

4 • 3 = 122 2

x = yx = y

DIVISION PROPERTY OF EQUALITY

Words Numbers Algebra

z

4 • 3 = 12

z 6 = 6

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 8x = 32.

Example 1: Solving Equations Using Division

8x = 32

1x = 4

Divide both sides by 8.

Check

8x = 328 8

x = 4

8x = 328(4) = 32?

32 = 32? Substitute 4 for x.

1 • x = x

1-4 Solving Multiplication and Division Equations

Pre-Algebra

You can multiply both sides of an equation by the same number, and the statement will still be true.

2 • 3 = 6x = yx = yz z

MULTIPLICATION PROPERTY OF EQUALITY

Words Numbers Algebra

2 • 3 = 6 4 • 4 •

8 • 3 = 24

You can solve a division equation using the Multiplication Property of Equality.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve = 7.

Example 2: Solving Equations Using Multiplication

n7n7 = 77 • 7 • Multiply both sides by 7.

n = 49

Checkn7 = 7

Substitute 49 for n.497 = 7

?

7 = 7?

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Multiplication and division are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

You can solve a multiplication equation using the Division Property of Equality.

You can divide both sides of an equation by the same nonzero number, and the equation will still be true.

4 • 3 = 122 2

x = yx = y

DIVISION PROPERTY OF EQUALITY

Words Numbers Algebra

z

4 • 3 = 12

z 6 = 6

1-4 Solving Multiplication and Division Equations

Pre-Algebra

You can solve a multiplication equation using the Division Property of Equality.

You can divide both sides of an equation by the same nonzero number, and the equation will still be true.

4 • 3 = 122 2

x = yx = y

DIVISION PROPERTY OF EQUALITY

Words Numbers Algebra

z

4 • 3 = 12

z 6 = 6

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 9x = 36.

Try This: Example 1

9x = 36

1x = 4

Divide both sides by 9.

Check

9x = 369 9

x = 4

9x = 369(4) = 36?

36 = 36? Substitute 4 for x.

1 • x = x

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve = 16

Try This: Example 2

n4n4 = 164 • 4 • Multiply both sides by 4.

n = 64

Checkn4 = 16

Substitute 64 for n.644 = 16

?

16 = 16?

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Example 3: Food Application

Ace has enough flour to bake one sheet cake but would rather make cookies. How many dozen cookies can he make?

Dessert

Apple crisp

Bread pudding

Cookies (1 doz.)

Pumpkin pie

Sheet cake

Tiramisu

Cups of Flour

1.5

4

2

1

8

3

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Example 3 Continued

cups of flour for 1 dozen cookies

cups of flour in 1 cake• =

number of dozen cookies

2 • =c 8

2c = 82 2c = 4

Ace can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake.

Write the equation.

Divide both sides by 2.

2c = 8

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Example 4: Money Application

fraction of amount raised so far

amount raised so far• =

• =x 50

4 •

x = 200

Faith has saved $50, which is one-fourth of the amount she needs for a school trip. What is the total amount she needs?

Write the equation.

Multiply both sides by 4.

total amount needed

14

x = 5014

4 • x = 5014

Olivia needs $200 total.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Sometimes it is necessary to solve equations by using two inverse operations. For instance, the

equation 6x − 2 = 10 has multiplication and subtraction.

6x − 2 = 10

Variable term

Subtraction

Multiplication

To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 3y – 7 = 20.

Example 5: Solving a Simple Two-Step Equation

3y – 7 = 20Step 1: Add 7 to both sides to isolate the term with y in it.+ 7 + 7

3y = 27

Step 2: 3y = 273 3 y = 9

Divide both sides by 3.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 4y + 5 = 29.

Example 5: Solving a Simple Two-Step Equation

4y + 5 = 29Step 1: Subtract 5 from both sides to isolate the term with y in it.– 5 – 5

4y = 24

Step 2: 4y = 244 4 y = 6

Divide both sides by 4.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Addition and subtraction are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Multiplication and division are inverse operations, which means they “undo” each other.

To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 9x = 36.

Try This: Example 1

9x = 36

1x = 4

Divide both sides by 9.

Check

9x = 369 9

x = 4

9x = 369(4) = 36?

36 = 36? Substitute 4 for x.

1 • x = x

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve = 16

Try This: Example 2

n4n4 = 164 • 4 • Multiply both sides by 4.

n = 64

Checkn4 = 16

Substitute 64 for n.644 = 16

?

16 = 16?