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2-7
MultiplicationEquations
Equations
2-7 Multiplication
Warm Up
Problem of the Day
Lesson Presentation
Course
1
Course 11
Course
2-7 Multiplication Equations
Warm Up
Divide.
72
1. 12
3. 60
6
6
13
2. 65
5
10
4. 40 4
10
5. 130 26
5
Course 1
6. 91 13
7
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 = 32
4
4
m=8
Course 1
Caution !
4m means “4  m.”
2-7 Multiplication Equations
Additional Example 1A: Solving Multiplication
Equations
Solve the equation. Check your answer.
5p = 75
p is multiplied by 5.
5p = 75
5
5
Divide both sides by 5 to undo
the multiplication.
p = 15
Check 5p = 75
?
5(15)= 75
?
75 = 75 
Course 1
Substitute 15 for p in the equation.
15 is the solution.
2-7 Multiplication Equations
Additional Example 1B: Solving Multiplication
Equations
Solve the equation. Check your answer.
16 =
16 =
8
2=
8r
8r
8
r
r is multiplied by 8.
Divide both sides by 8 to undo
the multiplication.
Check 16 = 8r
?
16 = 8(2)
?
16 = 16 
Course 1
Substitute 2 for r in the equation.
2 is the solution.
2-7 Multiplication Equations
Check It Out: Example 1A
Solve the equation. Check your answer.
8a = 72
a is multiplied by 8.
8a = 72
8
8
x=9
Divide both sides by 8 to undo
the multiplication.
Check 8a = 72
?
8(9)= 72
?
72 = 72 
Course 1
Substitute 9 for a in the equation.
9 is the solution.
2-7 Multiplication Equations
Check It Out: Example 1B
Solve the equation. Check your answer.
w is multiplied by 3.
18 = 3w
18 = 3w
3
3
6=w
Divide both sides by 3 to undo
the multiplication.
Check 18 = 3w
?
18 = 3(6)
?
18 = 18 
Course 1
Substitute 6 for w in the equation.
6 is the solution.
2-7 Multiplication Equations
Additional Example 2: Problem Solving Application
The area of a rectangle is 56 square
inches. Its length is 8 inches. What
is its width?
Course 1
2-7 Multiplication Equations
Additional Example 2 Continued
1
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
Course 1
w
2-7 Multiplication Equations
Additional Example 2 Continued
2
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.
A = lw
56 = 8w
w
l
Course 1
2-7 Multiplication Equations
Additional Example 2 Continued
3
Solve
56 = 8w
56 = 8w
8
8
7=w
w is multiplied by 8.
Divide both sides by 8 to undo
the multiplication.
So the width of the rectangle is 7 inches.
Course 1
2-7 Multiplication Equations
Additional Example 2 Continued
4
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.
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
1
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
Course 1
8
2-7 Multiplication Equations
Check It Out: Example 2 Continued
2
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.
A = lw
48 = l8
w
l
Course 1
2-7 Multiplication Equations
Check It Out: Example 2 Continued
3
Solve
48 = 8l
48 = 8l
8
8
6=l
l is multiplied by 8.
Divide both sides by 8 to undo
the multiplication.
So the length of the rectangle is 6 inches.
Course 1
2-7 Multiplication Equations
Check It Out: Example 2 Continued
4
Course 1
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.
2-7 Multiplication Equations
Lesson Quiz
1. 10y = 300
y = 30
2. 2y = 82
y = 41
3. 63 = 9y
y=7
4. 78 = 13x
x=6
5. The area of a board game is 468 square inches.
Its width is 18 inches. What is the length?
26 inches
Course 1
Equations
2-7
Division Equations
2-8 Multiplication
Warm Up
Problem of the Day
Lesson Presentation
Course
1
Course 11
Course
Division Equations
Equations
2-7 Multiplication
2-8
Warm Up
Solve.
5x = 20
x 1.
=4
n2.
= 7n
12 = 84
y3.=18
22= y – 4
4.
2118
=n+3
n=
Course 1
1
Course
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
Additional Example 1A: Solving Division Equations
Solve the equation. Check your answer.
x
=5
7
x =5
7
7 x
= 7 5
7
x = 35
x =5
Chec 7
?
k
35 =
5
7
?
5 = 5
Course 1
x is divided by 7.
Multiply both sides by 7 to
undo the division.
Substitute 35 for x in the equation.
35 is the solution.
2-7 Multiplication Equations
Additional Example 1B: Solving Division Equations
Solve the equation. Check your answer.
13 = p
6
13 = p
p is divided by 6.
6
6  13 = 6  p
Multiply both sides by 6 to
6
undo the division.
78 = p
p
13
=
Chec
6
k
?
13 = 78
Substitute 78 for p in the equation.
6
?
13 = 13
 78 is the solution.
Course 1
2-7 Multiplication Equations
Check It Out: Example 1A
Solve the equation. Check your answer.
x
=9
2
x =9
x is divided by 2.
2
Multiply both sides by 2 to
2 x
= 2 9
2
undo the division.
x = 18
x =9
Chec 2
?
k
18 =
9
2
?
9 = 9
Course 1
Substitute 18 for x in the equation.
18 is the solution.
2-7 Multiplication Equations
Check It Out: Example 1B
Solve the equation. Check your answer.
72 = p
4
72 = p
p is divided by 4.
4
4  72 = 4  p
Multiply both sides by 4 to
4
undo the division.
288 = p
p
72
=
Chec
4
k
?
72 = 288
Substitute 288 for p in the equation.
4
?
72 = 72
 288 is the solution.
Course 1
2-7 Multiplication Equations
Additional Example 2: Application
At Elk Meadows Park an aspen tree is onethird the height of a pine tree.
height of aspen = height of pine
3
The aspen tree is 14 feet tall. How tall is the
pine tree?
Let h represent the height of the pine tree.
Substitute 14 for height of
14 = h
3
aspen. h is divided by 3.
Multiply both sides by 3 to
3  14 = 3  h
3
undo the division.
42 = h
The pine tree is 42 feet tall.
Course 1
2-7 Multiplication Equations
Check It Out: Example 2
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?
Let w represent her father’s weight.
Substitute 95 for Jamie’s
95 = w
2
weight. w is divided by 2.
2  95 =2  w
Multiply both sides by 2 to
2
undo the division.
190 = w
Jamie’s father weighs 190 pounds.
Course 1
2-7 Multiplication Equations
Lesson Quiz
Solve each equation. Check your answers.
x
10
1. x ==70
7
x 2.x 8==32
43.
= 11
4. x ==99
7
x
9
x
x = 105
15
5. The area of Sherry’s flower garden is onefourth the area of her vegetable garden. The
area of the flower garden is 17 square feet. Let x
represent the area of her vegetable garden. Find
68 square feet
the area of her vegetable garden?
Course 1