Download Divide both sides by 8 to undo the multiplication

1-10
Solving Equations by Dividing
California
Standards
AF1.1 Write and solve one-step
linear equations in one variable.
Holt CA Course 1
1-10
Solving Equations by Dividing
Dividing by a number is the inverse of
multiplying by that number. To solve an
equation that contains multiplication, use
division to “undo” the multiplication.
4m = 32
4m = 32
4
4
m=8
Holt CA Course 1
Caution !
4m means “4  m.”
1-10
Solving Equations by Dividing
Example 1A: Solving Equations by Dividing
Solve the equation. Check your answer.
5p = 75
p is multiplied by 5.
5p = 75
5
5
p = 15
Divide both sides by 5 to undo
the multiplication.
Check 5p = 75
?
5(15)= 75
?
75 = 75 
Holt CA Course 1
Substitute 15 for p in the
equation.
15 is the solution.
1-10
Solving Equations by Dividing
Example 1B: Solving Equations by Dividing
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 
Holt CA Course 1
Substitute 2 for r in the equation.
2 is the solution.
1-10
Solving Equations by Dividing
Example 2: Problem Solving Application
The area of a rectangle is 56 square
inches. Its length is 8 inches. What
is its width?
Remember!
For a rectangle,
area = length  width
Holt CA Course 1
1-10
Solving Equations by Dividing
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.
8
w
56
Holt CA Course 1
1-10
Solving Equations by Dividing
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
Holt CA Course 1
1-10
Solving Equations by Dividing
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.
Holt CA Course 1
1-10
Solving Equations by Dividing
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.
Holt CA Course 1
1-10
Solving Equations by Dividing
Check It Out! Example 1
Solve the equation. Check your answer.
8a = 72
a is multiplied by 8.
8a = 72
8
8
a=9
Divide both sides by 8 to undo
the multiplication.
Check 8a = 72
?
8(9)= 72
?
72 = 72 
Holt CA Course 1
Substitute 9 for a in the equation.
9 is the solution.
1-10
Solving Equations by Dividing
Check It Out! Example 2
The area of a rectangle is 48 square
inches. Its width is 8 inches. What is
its length?
Holt CA Course 1
1-10
Solving Equations by Dividing
Check It Out! Example 2 Continued
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
Holt CA Course 1
8
1-10
Solving Equations by Dividing
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
Holt CA Course 1
1-10
Solving Equations by Dividing
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.
Holt CA Course 1
1-10
Solving Equations by Dividing
Check It Out! Example 2 Continued
4
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.
Holt CA Course 1