![Page 1: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/1.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing1-3Solving Equations by
Multiplying or Dividing
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 1
![Page 2: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/2.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Warm Up
Evaluate each expression.
1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
4.
5.
6.
19.6
0.16
1
81
23
1.8
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Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve one-step equations in one variable by
using multiplication or division.
Objective
![Page 4: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/4.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Inverse Operations
Operation Inverse Operation
Multiplication Division
Division Multiplication
Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.
![Page 5: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/5.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation.
Example 1A: Solving Equations by Using
Multiplication
Since j is divided by 3,
multiply both sides by 3
to undo the division.–24 = j
–8 –8
To check your solution,
substitute –24 for j in the
original equation.
–8 =j
3
–8–24
3
Check –8 =j
3
![Page 6: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/6.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation.
Example 1B: Solving Equations by Using
Multiplication
Since n is divided by 6,
multiply both sides by 6
to undo the division.n = 16.8
2.8 2.8
To check your solution,
substitute 16.8 for n in the
original equation.
= 2.8n
6
2.816.8
6
Check = 2.8n
6
![Page 7: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/7.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 1a
Since p is divided by 5,
multiply both sides by 5
to undo the division.p = 50
10 10
To check your solution,
substitute 50 for p in the
original equation.
= 10p
5
1050
5
Check = 10p
5
![Page 8: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/8.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 1b
Since y is divided by 3,
multiply both sides by 3 to
undo the division.–39 = y
–13 –13
To check your solution,
substitute –39 for y in the
original equation.
–13 =y
3
–13–39
3
yCheck –13 =
3
![Page 9: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/9.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 1c
Since c is divided by 8,
multiply both sides by 8
to undo the division.c = 56
7 7
To check your solution,
substitute 56 for c in the
original equation.
= 7c
8
756
8
Check = 7c
8
![Page 10: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/10.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Example 2A: Solving Equations by Using Division
Since y is multiplied by 9,
divide both sides by 9 to
undo the multiplication.y = 12
108 108
To check your solution,
substitute 12 for y in the
original equation.
9y = 108
9(12) 108
Check 9y = 108
![Page 11: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/11.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Example 2B: Solving Equations by Using Division
Since v is multiplied by –6,
divide both sides by –6 to
undo the multiplication.0.8 = v
–4.8 –4.8
To check your solution,
substitute 0.8 for v in the
original equation.
–4.8 = –6v
–4.8 –6(0.8)
Check –4.8 = –6v
![Page 12: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/12.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2a
Since c is multiplied by 4,
divide both sides by 4 to
undo the multiplication.4 = c
16 16
To check your solution,
substitute 4 for c in the
original equation.
16 = 4c
16 4(4)
Check 16 = 4c
![Page 13: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/13.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2b
Since y is multiplied by 0.5,
divide both sides by 0.5 to
undo the multiplication.y = –20
–10 –10
To check your solution,
substitute –20 for y in the
original equation.
0.5y = –10
0.5(–20) –10
Check 0.5y = –10
![Page 14: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/14.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2c
Since k is multiplied by 15,
divide both sides by 15 to
undo the multiplication.k = 5
75 75
To check your solution,
substitute 5 for k in the
original equation.
15k = 75
15(5) 75
Check 15k = 75
![Page 15: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/15.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.
![Page 16: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/16.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation.
Example 3A: Solving Equations That Contain
Fractions
w = 24
20 20
To check your solution,
substitute 24 for w in the
original equation.
w = 2056
Check w = 205
6
The reciprocal of is . Since w is
multiplied by , multiply both sides
by .
56
65
56
65
20
![Page 17: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/17.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation.
Example 3B: Solving Equations That Contain
Fractions
= z3
16
To check your solution,
substitute for z in the
original equation.
32
= z32
18 The reciprocal of is 8. Since z is
multiplied by , multiply both sides
by 8.
18
18
Check1
8
316
= z
3
16
3
16
![Page 18: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/18.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 3a
– = b14
To check your solution,
substitute – for b in the
original equation.
54
15
The reciprocal of is 5. Since b is
multiplied by , multiply both sides
by 5.
15
15
= b54
–
= b54Check11–
![Page 19: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/19.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Check It Out! Example 3b
j = 1
Solve the equation.
=4j6
23
is the same as j.46
4j
6
The reciprocal of is . Since j is
multiplied by , multiply both sides
by .
46
46
64
64
![Page 20: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/20.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Check It Out! Example 3b Continued
To check your solution,
substitute 1 for j in the
original equation.
Check2
3
4j6
=
Solve the equation.
=4j6
23
![Page 21: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/21.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
w = 712
102 102
To check your solution,
substitute 712 for w in the
original equation.
w = 10216
Check w = 1021
6
The reciprocal of is 6. Since w is
multiplied by , multiply both sides
by 6 .
16
16
Solve the equation.
Check It Out! Example 3c
102
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Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Example 4: Application
Write an equation to represent the relationship.
Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year.
14
one-fourth times earnings equals college fund
m = $1140
Substitute 285 for c. Since m is divided
by 4, multiply both sides by 4 to undo
the division.
Ciro earned $1140 mowing lawns.
![Page 23: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/23.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Check it Out! Example 4
Write an equation to represent the
relationship.
The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began.
Distance divided by 3 equals height in thousands of feet
15 = h
Substitute 45 for d.
The plane was flying at 15,000 ft when the descent began.
![Page 24: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/24.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
WORDS
Addition Property of Equality
You can add the same number to both sides of an equation, and the statement will still be true.
NUMBERS
3 = 3
3 + 2 = 3 + 2
5 = 5
ALGEBRAa = b
a + c = b + c
Properties of Equality
![Page 25: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/25.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
WORDS
Subtraction Property of Equality
You can subtract the same number from both sides of an equation, and the statement will still be true.
NUMBERS
7 = 7
7 – 5 = 7 – 5
2 = 2
ALGEBRAa = b
a – c = b – c
Properties of Equality
![Page 26: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/26.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
WORDS
Multiplication Property of Equality
You can multiply both sides of an equation by the same number, and the statement will still be true.
NUMBERS
6 = 6
6(3) = 6(3)
18 = 18
ALGEBRAa = b
ac = bc
Properties of Equality
![Page 27: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/27.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Properties of EqualityDivision Property of Equality
You can divide both sides of an equation by the same nonzero number, and the statement will still be true.
WORDS
a = b(c ≠ 0)
8 = 8
2 = 2
ALGEBRA
NUMBERS 8
4
8
4=
ac
ac
=
![Page 28: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/28.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Lesson Quiz: Part 1
Solve each equation.
1.
2.
3. 8y = 4
4. 126 = 9q
5.
6.
21
2.8
–14
40
![Page 29: 1-3 Solving Equations by Multiplying or Dividing€¦ · Multiplying or Dividing Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division Since y is](https://reader034.vdocuments.us/reader034/viewer/2022051812/602fc488ad356f7d40522eba/html5/thumbnails/29.jpg)
Holt McDougal Algebra 1
1-3Solving Equations by
Multiplying or Dividing
Lesson Quiz: Part 2
7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.
9
10