Course 1

2-7 Multiplication Equations

Course 1

2-7 Multiplication Equations

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

2-7 Multiplication Equations

Warm UpDivide.

1. 2.

3. 4.

5. 6.

6 13

10 4

7212

655

606

4010

1305

91726 13

Course 1

2-7 Multiplication Equations

Problem of the Day

Katie’s little brother is building a tower with blocks. He adds 6 blocks and then removes 4 blocks. If he adds 8 more blocks, the tower will have twice as many blocks as when he started. How many blocks did he start with?10 blocks

Course 1

2-7 Multiplication Equations

Learn to solve whole-number multiplication equations.

Course 1

2-7 Multiplication Equations

Division is the inverse of multiplication. To solve an equation that contains multiplication, use division to “undo” the multiplication.

4m = 32

4m = 324 4 m = 8

Caution !Caution !

4m means “4 m.”

Course 1

2-7 Multiplication Equations

5p = 75 p is multiplied by 5.

5

p = 15

Divide both sides by 5 to undo the multiplication.

Check 5p = 75

Substitute 15 for p in the equation.

Solve the equation. Check your answer.

15 is the solution.75 = 75?

Additional Example 1A: Solving Multiplication Equations

5(15)= 75 ?

55p = 75

Course 1

2-7 Multiplication Equations

16 = 8r r is multiplied by 8.

82 = r

Divide both sides by 8 to undo the multiplication.

Check 16 = 8r

Substitute 2 for r in the equation.

Solve the equation. Check your answer.

2 is the solution.16 = 16?

Additional Example 1B: Solving Multiplication Equations

16 = 8(2) ?

816 = 8r

Course 1

2-7 Multiplication Equations

8a = 72 a is multiplied by 8.

8x = 9

Divide both sides by 8 to undo the multiplication.

Check 8a = 72

Substitute 9 for a in the equation.

Solve the equation. Check your answer.

9 is the solution.72 = 72?

Check It Out: Example 1A

8(9)= 72?

88a = 72

Course 1

2-7 Multiplication Equations

18 = 3w w is multiplied by 3.

36 = w

Divide both sides by 3 to undo the multiplication.

Check 18 = 3w

Substitute 6 for w in the equation.

Solve the equation. Check your answer.

6 is the solution.18 = 18?

Check It Out: Example 1B

18 = 3(6) ?

318 = 3w

Course 1

2-7 Multiplication Equations

The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width?

Additional Example 2: Problem Solving Application

Course 1

2-7 Multiplication Equations

Additional Example 2 Continued11 Understand the Problem

The answer will be the width of the rectangle in inches.

List the important information:

• The area of the rectangle is 56 square inches.• The length of the rectangle is 8 inches.

Draw a diagram to represent this information.

56

8

w

Course 1

2-7 Multiplication Equations

Additional Example 2 Continued

22 Make a Plan

You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width.

w

l

A = lw56 = 8w

Course 1

2-7 Multiplication Equations

Additional Example 2 Continued

56 = 8w56 = 8w

Solve33

8 87 = w

So the width of the rectangle is 7 inches.

w is multiplied by 8.Divide both sides by 8 to undo the multiplication.

Course 1

2-7 Multiplication Equations

Additional Example 2 Continued

Look Back

Arrange 56 identical squares in a rectangle. The length is 8, so line up the squares in rows of 8. You can make 7 rows of 8, so the width of the rectangle is 7.

44

Course 1

2-7 Multiplication Equations

Check It Out: Example 2

The area of a rectangle is 48 square inches. Its width is 8 inches. What is its length?

Course 1

2-7 Multiplication Equations

Check It Out: Example 2

11 Understand the Problem

The answer will be the length of the rectangle in inches.

List the important information:• The area of the rectangle is 48 square inches.• The width of the rectangle is 8 inches.

Draw a diagram to represent this information.

48

l

8

Course 1

2-7 Multiplication Equations

Check It Out: Example 2 Continued

22 Make a Plan

You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width.

w

l

A = lw48 = l8

Course 1

2-7 Multiplication Equations

Check It Out: Example 2 Continued

48 = 8l48 = 8l

Solve33

8 86 = l

So the length of the rectangle is 6 inches.

l is multiplied by 8.Divide both sides by 8 to undo the multiplication.

Course 1

2-7 Multiplication Equations

Check It Out: Example 2 Continued

Look Back

Arrange 48 identical squares in a rectangle. The width is 8, so line up the squares in columns of 8. You can make 6 columns of 8, so the length of the rectangle is 6.

44

Course 1

2-7 Multiplication Equations

1. 10y = 300

2. 2y = 82

3. 63 = 9y

4. 78 = 13x

Lesson Quiz

5. The area of a board game is 468 square inches. Its width is 18 inches. What is the length?

y = 30

y = 41

y = 7

x = 6

26 inches

Course 1

2-7 Multiplication Equations

Course 1

2-8 Division Equations

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

2-7 Multiplication Equations

Warm UpSolve.

1. 5x = 20

2. 7n = 84

3. 18 = y – 4

4. 21 = n + 3

x = 4

n = 12

y = 22

n = 18

Course 1

2-8 Division Equations

Course 1

Course 1

2-7 Multiplication Equations

Problem of the Day

If 11 is 4 less than 3 times a number, what is the number?

5

Course 1

2-7 Multiplication Equations

Learn to solve whole-number division equations.

Course 1

2-7 Multiplication Equations

Multiplication is the inverse of division. When an equation contains division, use

multiplication to “undo” the division.

Course 1

2-7 Multiplication Equations

x = 35

Multiply both sides by 7 to undo the division.

Substitute 35 for x in the equation.

Solve the equation. Check your answer.

35 is the solution.5 = 5?

Additional Example 1A: Solving Division Equations

x7

= 5

x is divided by 7. x7

= 5

7 x7

= 7 5

Check

x7

= 5 357

= 5?

Course 1

2-7 Multiplication Equations

78 = p

Multiply both sides by 6 to undo the division.

Substitute 78 for p in the equation.

Solve the equation. Check your answer.

78 is the solution.13 = 13?

Additional Example 1B: Solving Division Equations

p6

13 =

6 p6

6 13 =

p is divided by 6. p6

13 =

Check

p6

13 =

? 786

13 =

Course 1

2-7 Multiplication Equations

x = 18

Multiply both sides by 2 to undo the division.

Substitute 18 for x in the equation.

Solve the equation. Check your answer.

18 is the solution.9 = 9?

Check It Out: Example 1A

x2

= 9

x is divided by 2. x2

= 9

2 x2

= 2 9

Check

x2

= 9 182

= 9?

Course 1

2-7 Multiplication Equations

288 = p

Multiply both sides by 4 to undo the division.

Substitute 288 for p in the equation.

Solve the equation. Check your answer.

288 is the solution.72 = 72?

Check It Out: Example 1B

p4

72 =

4 p4

4 72 =

p is divided by 4. p4

72 =

Check

p4

72 =

? 2884

72 =

Course 1

2-7 Multiplication Equations

At Elk Meadows Park an aspen tree is one-third the height of a pine tree.

Additional Example 2: Application

height of aspen = height of pine3

The aspen tree is 14 feet tall. How tall is the pine tree?

Let h represent the height of the pine tree.

42 = h

Multiply both sides by 3 to undo the division.

3 h3

3 14 =

Substitute 14 for height of aspen. h is divided by 3.

h3

14 =

The pine tree is 42 feet tall.

Course 1

2-7 Multiplication Equations

Check It Out: Example 2

Let w represent her father’s weight.

190 = w

Multiply both sides by 2 to undo the division.

2 w2

2 95 =

Substitute 95 for Jamie’s weight. w is divided by 2.

w2

95 =

Jamie’s father weighs 190 pounds.

Jamie weighs one-half as much as her father.

Jamie’s weight = father’s weight 2

Jamie weighs 95 pounds. How many pounds does her father weigh?

Course 1

2-7 Multiplication Equations

1. = 72. 8 =

3. = 114. = 7

Lesson Quiz

5. The area of Sherry’s flower garden is one-fourth the area of her vegetable garden. The

area of the flower garden is 17 square feet. Let xrepresent the area of her vegetable garden. Find

the area of her vegetable garden?

x = 70

x = 32

x = 99

x = 105

68 square feet

x 4

x 9

Solve each equation. Check your answers.

x 10

x 15