3. 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
5. 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
Caution !
4m = 32
4m means “4 × m.”
4 4
m=8
Course 1
6. 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 Divide both sides by 5 to undo
5 5 the multiplication.
p = 15
Check 5p = 75
?
5(15)= 75 Substitute 15 for p in the equation.
?
75 = 75 15 is the solution.
Course 1
7. 2-7 Multiplication Equations
Additional Example 1B: Solving Multiplication
Equations
Solve the equation. Check your answer.
16 = 8r r is multiplied by 8.
16 = 8r Divide both sides by 8 to undo
8 8 the multiplication.
2= r
Check 16 = 8r
?
16 = 8(2) Substitute 2 for r in the equation.
?
16 = 16 2 is the solution.
Course 1
8. 2-7 Multiplication Equations
Check It Out: Example 1A
Solve the equation. Check your answer.
8a = 72 a is multiplied by 8.
8a = 72 Divide both sides by 8 to undo
8 8 the multiplication.
x=9
Check 8a = 72
?
8(9)= 72 Substitute 9 for a in the equation.
?
72 = 72 9 is the solution.
Course 1
9. 2-7 Multiplication Equations
Check It Out: Example 1B
Solve the equation. Check your answer.
18 = 3w w is multiplied by 3.
18 = 3w Divide both sides by 3 to undo
3 3 the multiplication.
6=w
Check 18 = 3w
?
18 = 3(6) Substitute 6 for w in the equation.
?
18 = 18 6 is the solution.
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10. 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?
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11. 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 w
8
Course 1
12. 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 w
56 = 8w
l
Course 1
13. 2-7 Multiplication Equations
Additional Example 2 Continued
3 Solve
56 = 8w w is multiplied by 8.
56 = 8w Divide both sides by 8 to undo
8 8 the multiplication.
7=w
So the width of the rectangle is 7 inches.
Course 1
14. 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
15. 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?
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16. 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 8
l
Course 1
17. 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 w
48 = l8
l
Course 1
18. 2-7 Multiplication Equations
Check It Out: Example 2 Continued
3 Solve
48 = 8l l is multiplied by 8.
48 = 8l Divide both sides by 8 to undo
8 8 the multiplication.
6=l
So the length of the rectangle is 6 inches.
Course 1
19. 2-7 Multiplication Equations
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.
Course 1
20. 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
