Download Solving Multiplication and Division Equations

Page 1 of 4
Solving Multiplication
and Division Equations
BEFORE
Now
WHY?
You solved one-step addition
and subtraction equations.
You’ll solve multiplication and
division equations.
So you can make predictions about
a hurricane’s travel time, as in Ex. 33.
You can use algebra tiles to solve a multiplication
equation.
Word Watch
Review Words
variable, p. 29
solution, p. 36
solve, p. 37
1 Use algebra tiles to represent the
equation 2x 6.
2 Divide the x-tiles into two equal
groups. Divide the 1-tiles into the
same number of equal groups.
3 Match a group on the left with a
group on the right. Explain how this
tells you the solution of the equation.
Use algebra tiles to solve the equation.
1. 2x 8
2. 3x 9
3. 4x 12
The activity shows how you can solve a multiplication equation using
algebra tiles. You can also use division to solve a multiplication equation.
EXAMPLE
1
Solving a Multiplication Equation
Solve the equation 5x 20.
with
Review
As you saw on page 253,
the fraction bar is a
way to express division.
You will write division
using a fraction bar when
you solve multiplication
and division equations.
5x 20
Write the original equation.
5x
20
5
5
Divide each side by 5.
x4
Your turn now
1. 4n 20
598
Chapter 12
Equations and Functions
Simplify.
Solve the equation. Then check the solution.
2. 3m 15
3. 24 2p
4. 65 5q
Page 2 of 4
Solving Multiplication and Division Equations
You can use multiplication and division to undo each other
when trying to get the variable by itself on one side of an
equation.
Multiplication Equations To solve a multiplication equation,
divide each side by the number the variable is multiplied by.
Division Equations To solve a division equation, multiply
each side by the divisor.
EXAMPLE
2
Solving a Division Equation
x
7
Solve the equation 3.
x
3
7
x
7 p 7 p 3
7
x 21
EXAMPLE
3
Write the original equation.
Multiply each side by 7.
Simplify.
Using an Equation
Cheerleading In cheerleader tryouts, 27 students are placed in groups of
3 to make human pyramids. Write and solve a multiplication equation to
find n, the number of pyramids the 27 students form.
Solution
27 3n
Write an equation.
27
3n
3
3
Divide each side by 3.
9n
Simplify.
ANSWER The 27 students will form 9 pyramids.
Your turn now
a
5. 7
2
Solve the equation. Then check the solution.
b
6. 6
5
Lesson 12.4
c
7. 45 3
d
8. 12 8
Solving Multiplication and Division Equations
599
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 719
Getting Ready to Practice
1. Vocabulary You can solve a multiplication equation by _?_. You can
solve a division equation by _?_.
Solve the equation. Then check the solution.
2. 5x 35
3. 14 7y
c
5. 2
6
a
4. 14 2
In Exercises 6 and 7, write the sentence as an equation. Then
solve the equation.
6. Five times a number x is 105.
7. 24 is a number c divided by 2.
8. Pretzels You purchase 8 soft pretzels for your friends. You pay $14.
Write a multiplication equation you can use to find the cost of a soft
pretzel. Then solve the equation.
Practice and Problem Solving
Copy and complete the solution.
x
4
9
9. 5x 10
10. 27 9x
5x
10
?
?
27
9x
?
?
_?_ p _?_ p 4
x _?_
_?_ x
x _?_
11.
x
9
Solve the equation.
with
Example
1
2
3
Homework
Exercises
9, 10, 12–19
11, 20–27
28–34
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
12. 4m 32
13. 3n 60
14. 5p 0
15. 7q 63
16. 35 7g
17. 42 3h
18. 72 6j
19. 51 17k
t
20. 12
10
a
24. 5 4
u
21. 10
5
b
25. 12 7
w
22. 15
6
c
26. 9 30
x
23. 4
21
d
27. 7 14
In Exercises 28–31, write the sentence as an equation. Then solve
the equation.
28. 112 is 8 times a number y.
29. Eleven times a number b is 44.
30. A number f divided by 6 is 9.
31. 27 is a number n divided by 3.
32. Pens Four friends share a box of pens. Each receives 3 pens. Write and
solve a division equation to find the number of pens in the box.
600
Chapter 12
Equations and Functions
Page 4 of 4
33. Hurricanes A hurricane is traveling at an average speed of 24 miles per
hour. Write and solve a multiplication equation to predict how many
hours it will take to travel 1728 miles if it continues at this speed.
Science
34. Sports A team won 45% of its games this year. The team won 9 games.
Write and solve a multiplication equation to find the number of games
the team played.
35. Critical Thinking Explain why you can multiply each side of the
1
1
equation x 20 by the reciprocal of to solve the equation.
4
4
Solve the equation.
36. 5m 28
37. 40 9p
39. 8q 56
40. 450 10s
x
38. 2.7
4
w
41. 4
5
42. Challenge An acre covers 43,560 square feet. The unit is based on early
■
Hurricanes
The product of a hurricane’s
speed (in miles per hour)
and its rainfall (in inches) is
about 100. What rainfall can
you expect from a storm
traveling 5 miles per hour?
farmers’ fields that were 10 times as long as they were wide. Find 10x
and x, the length and width, in feet, of such a field.
A 43,560 ft2
x
10x
Mixed Review
Evaluate the expression when x 3. (Lesson 1.5)
43. 5x 4
44. 8 7x
45. 30 3x
Solve the equation. (Lesson 12.3)
46. b 8 17
47. x 12 5
48. 41 m 19
Basic Skills Copy and complete the statement using <, >, or .
3
3
49. _?_ 8
4
8
1
51. _?_ 16
2
7
2
50. _?_ 9
3
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
52. Multiple Choice Solve the equation 12x 120.
A. 10
B. 108
C. 132
z
53. Multiple Choice Solve the equation 7.
8
7
F. G. 8
H. 15
8
Lesson 12.4
D. 1440
I. 56
Solving Multiplication and Division Equations
601