Page 1 of 5
Solving Multiplication and
Division Equations
BEFORE
Now
WHY?
You solved addition and
subtraction equations.
You’ll solve multiplication and
division equations.
So you can find the cost of a
telephone call, as in Ex. 32.
In the Real World
Word Watch
Review Words
inverse operations, p. 327
Flying Disc You throw a flying disc
to your dog. It stays in the air for
2.5 seconds before your dog catches it
30 feet away from you. In Example 4,
you’ll write and solve a multiplication
equation to find the speed of the disc.
Because multiplication and division are
inverse operations, you can use division
to solve a multiplication equation.
Division Property of Equality
Words Dividing each side of an equation by the same
nonzero number produces an equivalent equation.
Algebra ax b (a 0)
EXAMPLE
1
b
ax
a
a
Solving a Multiplication Equation
Solve 3x 45.
3x 45
Write original equation.
45
3x
3
3
Divide each side by 3.
x 15
✓Check
Simplify.
3x 45
3(15) 45
45 45 ✓
Lesson 7.4
Write original equation.
Substitute 15 for x.
Solution checks.
Solving Multiplication and Division Equations
333
Page 2 of 5
Multiplication Property of Equality
Words Multiplying each side of an equation by the same
nonzero number produces an equivalent equation.
x
Algebra b (a ≠ 0)
a
EXAMPLE
with
Notetaking
In your notebook, you
may want to compare
and contrast solving
multiplication and division
equations. This will help
you remember how to
solve these types of
equations.
2
x
a
a p a p b
Solving a Division Equation
x
2
Solve 0.75.
x
0.75
2
Write original equation.
x
2
Multiply each side by 2.
x 1.5
Simplify.
2 p 2 p 0.75
When you are solving an equation containing a fractional coefficient,
multiply each side of the equation by the reciprocal of the coefficient.
EXAMPLE
3
Solving an Equation Using a Reciprocal
2
3
Solve 4 x.
with
2
3
4 x
Review
Need help multiplying by
a reciprocal? See p. 222.
32(4) 32 23x
6 x
Your turn now
334
Chapter 7
Write original equation.
3
2
Multiply each side by .
Simplify.
Solve the equation. Check your solution.
1. 6a 54
2. 13b 65
d
3. 3.4 5
c
4. 13
2
5. 5p 3p 4
6. 16 s
4
7. r 1
5
2
8. 2 t
5
Equations, Inequalities, and Functions
Page 3 of 5
EXAMPLE
4
Writing and Solving an Equation
To find the speed of the flying disc described on page 333, use the
formula d rt.
Your dog catches the disc 30 feet from you, so the distance the disc
travels is 30 feet. The disc spends 2.5 seconds in the air.
d rt
30 r(2.5)
30
2.5r
2.5
2.5
12 r
Write formula for distance.
Substitute 30 for d and 2.5 for t.
Divide each side by 2.5.
Simplify.
ANSWER The speed of the disc is 12 feet per second.
Your turn now
Solve the following problem.
9. A DVD contains 7.5 hours of bonus material, which is 3 times longer
than the movie itself. Write and solve an equation to find the length
of the movie.
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Copy and complete: Multiplication and _?_ are inverse
operations.
Solve the equation. Check your solution.
2. 14q 42
3. 20r 100
4. 9s 27
5. 3t 9
w
6. 8
2
x
7. 12
6
3
8. y 12
4
3
9. z 6
10
10. Writing Write a real-world problem that can be solved using the
equation 5t 20.
11. Blimp A blimp travels 300 miles in 7.5 hours. Assuming that the blimp
travels at a constant speed, write and solve an equation to find the
speed of the blimp.
Lesson 7.4
Solving Multiplication and Division Equations
335
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
12–31, 37–44
12–31, 37–44
12–31, 37–44
32–33, 45, 48–49
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Describe how to solve each equation without actually solving.
12. 3x 15
13. 16x 4
x
14. 2
9
x
15. 7
15
Solve the equation. Check your solution.
16. 8p 24
17. 30b 5
18. b 12.5
19. 3.5f 24.5
20. 3 1.2y
21. 1.2s 6
r
22. 10
2
a
23. 4
3
d
24. 0.5
24
r
25. 36 5.5
z
26. 0.7 3
c
27. 11
14
4
28. t 12
3
5
29. y 5
7
1
30. w 12
2
3
31. 9 e
4
32. Telephone Bill Your telephone bill lists a call that lasted 18 minutes
and cost $1.08. Write and solve an equation to find how much you were
charged for each minute of the call.
33. Geometry A rectangle has a length of 7.5 meters
and an area of 45 square meters. Write and solve
an equation to find the rectangle’s width.
A 45 m 2 w
7.5 m
Write the verbal sentence as an equation. Then solve the equation.
34. The product of 10 and a number is 22.
35. Twice a number is equal to 100.
36. The quotient of a number and 3 is 6.6.
Solve the equation. Round the solution to the nearest hundredth if
necessary.
37. 3a 4
38. 14y 100 39. 22x 9
40. 1.65t 9.8
41. 3.6x 4.88
3
42. 2k
4
44. 6p 2p 9
43. 3 m 3m
45. Ski Lift A ski lift can carry 11,200 people in one day. The ski lift
operates from 9:00 A.M. to 4:00 P.M. each day. Write and solve an
equation to find the number of people the lift can carry in 1 hour.
46. Critical Thinking Is it possible to solve the equation 5x 29 by
multiplying each side of the equation by the same number? If so,
what is the number? Explain your reasoning.
47. Geometry The perimeter of a square is 32 inches. What is its area?
336
Chapter 7
Equations, Inequalities, and Functions
Page 5 of 5
Sports
Jump Rope In Exercises 48 and 49, use the following information.
Suppose that in the 3 minute speed event at a jump rope competition, a
jumper’s right foot strikes the ground 408 times. Assume that the jumper
keeps a steady pace.
48. Write and solve an equation to find the number of times the jumper’s
right foot strikes the ground in 1 minute.
49. How many times does the jumper’s right foot strike the ground in
1 second? Round your answer to the nearest tenth.
50. Challenge A mil is used to measure paper thickness. One mil is equal
to 0.001 inch. You have a stack of paper that is about 2.5 inches high.
Each sheet of paper is 11.8 mils thick. Write and solve an equation to
find the approximate number of sheets of paper in the stack.
51. Baseball The fastest recorded time for circling the 4 bases of a baseball
■
Jump Rope
In speed events at jump rope
competitions, the number of
times a jumper’s right foot
strikes the ground is counted.
The U.S. record for 12–14
year olds in the 2 minute
double dutch pairs speed
event is 715 right foot
strikes. About how many right
foot strikes were there in
1 second?
diamond is 13.3 seconds, set by Ernest Swanson in 1932. Consecutive
bases are 90 feet apart. Assuming that Swanson ran at a constant
speed, write and solve an equation to find Swanson’s speed, in feet per
second. Round your answer to the nearest tenth.
Mixed Review
Write the number in scientific notation. (Lesson 2.5)
52. 7000
53. 10,200
54. 504,060
55. 12,050,000
Solve the equation. Check your solution. (Lesson 7.3)
56. x 12 15
57. x 2 7
1
58. 5.2 x 8.6 59. x 5 2
Basic Skills Copy and complete.
60. 3540 sec _?_ min
61. 2.5 h _?_ min
62. 36 min _?_ h
63. 15,300 sec _?_ h
64. 12 h _?_ sec
65. 4.25 min _?_ sec
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
66. Extended Response The top female runner in the 2001 Boston
Marathon completed the 26.2 mile race in about 2 hours 24 minutes.
The top female wheelchair racer completed the race in about 1 hour
54 minutes. Convert both times to hours. If you assume that both
women traveled at a constant speed, find the speed of each woman, in
miles per hour, rounded to the nearest hundredth. About how much
faster was the speed of the wheelchair racer?
Lesson 7.4
Solving Multiplication and Division Equations
337