1-4 Solving Multiplication and Division Equations

Pre-Algebra

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Warm UpSolve.

x = 12n = 7

k = 1

t = 66

x = 13

1-4 Solving Multiplication and Division Equations

Pre-Algebra

5. 15 = x + 2

4. 47 = t 19

3. 5 + k = 6

2. 16 = n + 9

1. x 3 = 9

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Problem of the Day

Jackie went shopping for a new wardrobe. She bought seven new shirts and four new pairs of pants. She made sure that they can all be worn together in combinations. How many outfits can she put together? 28

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

Vocabulary

Division Property of EqualityMultiplication Property of Equality

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

12 = 62

z

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Solve 8x = 32.

Additional 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

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

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.

Additional 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

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

Additional Example 3: Food Application

Joe 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

Additional 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

Joe 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

Try This: Example 3

cups of flour for bread pudding

cups of flour in 1 cake

= number of bread pudding desserts

4 • =b 8

4b = 84 4c = 2

Joe can make 2 bread pudding desserts with the same amount of flour that he would need for 1 sheet cake.

Write the equation.

Divide both sides by 4.

4b = 8

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Additional Example 4: Money Application

fraction of amount raised so far

amount raised so far =

• =x 50

4 •

x = 200

Meg 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

Meg needs $200 total.

1-4 Solving Multiplication and Division Equations

Pre-Algebra

Try This: Example 4

amount raised so far =

• =x 750

8 •

x = 6000

The school library needs money to complete a new collection. So far, the library has raised $750, which is only one-eighth of what they need. What is the total amount needed?

Write the equation.

Multiply both sides by 8.

total amount needed

18

x = 75018

8 • x = 75018

The library needs to raise a total of $6000.

fraction of total amount raised so far

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.

Additional 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.

Try This: Example 5

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

Lesson Quiz

Solve.

1. = 3

2. 16t = 112

3. = 14

4. 3n + 17 = 29

5. Joan is making a scrapbook of her pictures. She wants to put three pictures on each page. She has 63 photos. Write and solve an equation to find how many pages she will need for all of the photos.

k = 18

n = 4

3x = 63; 21 pages

t = 7

b = 126

k6

b9