featurelesson pre-algebra lesson main properties of numbers lesson 2-1 at the red valley sports...
TRANSCRIPT
![Page 1: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/1.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Properties of NumbersProperties of Numbers
Lesson 2-1
At the Red Valley Sports Camp, 15 kids went horseback riding, 14played tennis, 23 went hiking, and the rest of the campers stayed intheir cabins. If 83 kids were in the camp, how many stayed indoors?
31
Problem of the Day
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Properties of NumbersProperties of Numbers
Lesson 2-1
(For help, go to Lesson 15.)
Simplify.
1. –18 + (–7) 2. 32 – (–3)
3. (–13) + 6 4. 2 – 48
Check Skills You’ll Need
Check Skills You’ll Need
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Properties of NumbersProperties of Numbers
Lesson 2-1
Solutions
1. –18 + (–7) = –25 2. 32 – (–3) = 32 + 3
= 35
32 – (–3) = 35
3. (–13) + 6 = –7 4. 2 – 48 = 2 + (–48)
= –46
2 – 48 = –46
Check Skills You’ll Need
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Carlos spent $42 on his golf game. He then bought
a bottle of water for $2 and a chef’s salad for $8. What was
the total cost for his golf game and meal?
Properties of NumbersProperties of Numbers
Lesson 2-1
42 + (2 + 8) = 42 + 10 = 52 Add 2 and 8 first.
Carlos’s total cost was $52.
You can use the Associative Property of Addition to find the total cost in two different ways.
(42 + 2) + 8 = 44 + 8 = 52 Add 42 and 2 first.
Quick Check
Additional Examples
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Name each property shown.
Properties of NumbersProperties of Numbers
Lesson 2-1
a. 17 + x + 3 = 17 + 3 + x
b. (36 2)10 = 36(2 10)
c. km = km • 1
d. (103 + 26) + 4 = 103 + (26 + 4)
Commutative Property of Addition
Associative Property of Multiplication
Identity Property of Multiplication
Associative Property of Addition
Quick Check
Additional Examples
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
![Page 7: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/7.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Use mental math to simplify (48 + 7) + 2.
Properties of NumbersProperties of Numbers
Lesson 2-1
(48 + 7) + 2
= (7 + 48) + 2 Use the Commutative Property of Addition.
= 7 + (48 + 2) Use the Associative Property of Addition.
= 7 + 50 Add within parentheses.
= 57 Add.
Quick Check
Additional Examples
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Suppose you buy school supplies costing $.45,
$.65, and $1.55. Use mental math to find the cost of these
supplies.
0.45 + 0.65 + 1.55
= 0.65 + 0.45 + 1.55 Use the Commutative Property of Addition.
= 0.65 + (0.45 + 1.55) Use the Associative Property of Addition.
= 0.65 + 2.00 Add within parentheses.
= 2.65 Add.
The cost of the school supplies is $2.65.
Properties of NumbersProperties of Numbers
Lesson 2-1
Quick Check
Additional Examples
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Use mental math to simplify (20 • 13) • 5.
Properties of NumbersProperties of Numbers
Lesson 2-1
(20 • 13) • 5 = (13 • 20) • 5 Use the Commutative Property of Multiplication.
= 13 • (20 • 5) Use the Associative Property of Multiplication.
= 13 • 100 Multiply within parentheses.
= 1,300 Multiply.
Quick Check
Additional Examples
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Properties of NumbersProperties of Numbers
Lesson 2-1
Name each property shown.
1. d 1 = d
2. 3 + (2 + 5) = (3 + 2) + 5
3. f g = g f
4. 32 + 45 + 102 = 45 + 32 + 102
Commutative Property of Multiplication
Identity Property of Multiplication
Associative Property of Addition
Commutative Property of Addition
Lesson Quiz
2-1
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
The Distributive PropertyThe Distributive Property
Lesson 2-2
Evaluate each expression.
a. 24 – 6 ÷ 2 • 4 + 36 b. 6 • (3 – 1) + 18 c. 10 + 6 • 5 – 4 ÷ 2
48 30 38
Problem of the Day
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
The Distributive PropertyThe Distributive Property
Lesson 2-2
(For help, go to Lesson 12.)
Simplify each expression.
1. 3 • 7 – 9 2. (9 – 5)6
3. 8 + 2 • 6 4. 2(6 – 3)
5. 4 • 5 – 4 • 3 6. 3 • 2 – 1 • 2
Check Skills You’ll Need
Check Skills You’ll Need
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
The Distributive PropertyThe Distributive Property
Lesson 2-2
Solutions
1. 3 • 7 – 9 2. (9 – 5) • 6
21 – 9 4 • 6
12 24
3. 8 + 2 • 6 4. 2 • (6 – 3)
8 + 12 2 • 3
20 6
5. 4 • 5 – 4 • 3 6. 3 • 2 – 1 • 2
20 – 12 6 – 2
8 4
Check Skills You’ll Need
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Use the Distributive Property to find 15(110) mentally.
The Distributive PropertyThe Distributive Property
Lesson 2-2
15(110) = 15(100 + 10) Write 110 as (100 + 10).
= 15 • 100 + 15 • 10 Use the Distributive Property.
= 1,500 + 150 Multiply.
= 1,650 Add.
Quick Check
Additional Examples
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Ms. Thomas gave 5 pencils to each of her 37
students. What is the total number of pencils she gave to
the students?
The Distributive PropertyThe Distributive Property
Lesson 2-2
(37)5 = (40 – 3)5 Write 37 as (40 – 3).
= 40 • 5 – 3 • 5 Use the Distributive Property.
= 200 – 15 Multiply.
= 185 Subtract.
Ms. Thomas gave the students 185 pencils.
Quick Check
Additional Examples
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplify 11(23) + 11(7).
The Distributive PropertyThe Distributive Property
Lesson 2-2
11(23) + 11(7) = 11(23 + 7) Use the Distributive Property.
= 11(30) Add within parentheses.
= 330 Multiply.
Quick Check
Additional Examples
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Use algebra tiles to multiply 4(3x – 4).
So 4(3x – 4) = 12x – 16.
The Distributive PropertyThe Distributive Property
Lesson 2-2
Model four groups of 3x – 4.
Group like tiles.
Quick Check
Additional Examples
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Multiply.
The Distributive PropertyThe Distributive Property
Lesson 2-2
a. –9(2 – 8y)
= –18 – (–72y) Multiply.
= –18 + 72y Simplify.
b. (5m + 6)11
= 55m + 66 Multiply.
–9(2 – 8y) = –9(2) – (–9)(8y) Use the Distributive Property.
(5m + 6)11 = (5m)11 + (6)11 Use the Distributive Property.
Quick Check
Additional Examples
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
The Distributive PropertyThe Distributive Property
Lesson 2-2
Use the Distributive Property to simplify.
1. 15(203) 2. 7(180)
3. 6(26) – 6(16) 4. (8a – 4)9
5. 2(14 + y)
60
3,045 1,260
28 + 2y
72a – 36
Lesson Quiz
2-2
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
Use numbers to write the following word expression: eight andone-third minus five and two-sevenths.
8 – 513
27
Problem of the Day
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
(For help, go to Lesson 2-2.)
Simplify each expression.
1. 5(b + 4) 2. –3(2x + 5)
3. 4(–8 – 3q) 4. –6(2b – 7)
Check Skills You’ll Need
Check Skills You’ll Need
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
Solutions
1. 5(b + 4) = 5(b) + 5(4) 2. –3(2x + 5) = –3(2x) + (–3)(5) = 5b + 20 = –6x – 15
3. 4(–8 – 3q) = 4(–8) + 4(–3q) 4. –6(2b – 7) = –6(2b) + (–6)(–7)
= –32 – 12q = –12b + 42
Check Skills You’ll Need
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Name the coefficients, the like terms, and the
constants in 7x + y – 2x – 7.
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
Coefficients: 7, 1, –2 Like terms: 7x, –2x Constant: –7
Quick Check
Additional Examples
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplify 9 + 4f + 3 + 2f.
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
9 + 4f + 3 + 2f 6f + 12
Quick Check
Additional Examples
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplify 2b + b – 4.
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
2b + b – 4 = 2b + 1b – 4 Use the Identity Property of Multiplication.
= (2 + 1)b – 4 Use the Distributive Property.
= 3b – 4 Simplify.
Quick Check
Additional Examples
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplify (7 – 3x)5 + 20x.
(7 – 3x)5 + 20x = 35 – 15x + 20x Use the Distributive Property.
= 35 + (–15x + 20x) Use the Associative Property of Addition.
= 35 + (–15 + 20)x Use the Distributive Propertyto combine like terms.
= 35 + 5x Simplify.
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
Quick Check
Additional Examples
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Simplifying Variable ExpressionsSimplifying Variable Expressions
Lesson 2-3
Name coefficients, like terms, and constants.
1. 4f – 2f + 3 2. z + 2y – 14
Simplify each expression.
3. 3(a + c – 1) – 2c 4. 4(4v) – 4(v – 9)
3a + c – 3
4, –2; 4f, –2f; 3 1, 2; none; –14
12v + 36
Lesson Quiz
2-3
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Variables and EquationsVariables and Equations
Lesson 2-4
Evaluate 10 – for c = 10.c5
8
Problem of the Day
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Variables and EquationsVariables and Equations
Lesson 2-4
(For help, go to Lesson 11.)
Write a variable expression for each phrase.
1. the sum of x and 46 2. four less than g
3. t decreased by five 4. the quotient of z and 26
Check Skills You’ll Need
Check Skills You’ll Need
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Variables and EquationsVariables and Equations
Lesson 2-4
Solutions
1. the sum of x and 46 2. four less than g x plus 46 g minus 4x + 46 g – 4
3. t decreased by five 4. the quotient of z and 26t minus 5 z divided by 26t – 5 z
26
Check Skills You’ll Need
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
State whether each equation is true, false, or an
open sentence. Explain.
Variables and EquationsVariables and Equations
Lesson 2-4
a. 3(b – 8) = 12
c. –9 + 5 = – 4
b. 7 – (–6) = 1
open sentence, because there is a variable
=/ false, because 13 1
true, because – 4 = – 4
Quick Check
Additional Examples
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Write an equation for Six times a number added to the
number is the opposite of forty-two. State whether the equation is
true, false, or an open sentence. Explain.
Variables and EquationsVariables and Equations
Lesson 2-4
The equation is an open sentence, because there is a variable.
Equation 6x + =x –42
six times the numberWords
6x
added to
added to x is
isthe oppositeof forty-two
–42
thenumber
Quick Check
Additional Examples
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Is 45 a solution of the equation 120 + x = 75?
Variables and EquationsVariables and Equations
Lesson 2-4
120 + x = 75
No, 45 is not a solution of the equation.
120 + 450 75 Substitute 45 for x.
165 75=/
Quick Check
Additional Examples
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
A gift pack must hold 20 lb of food. Apples weigh 9 lb and
cheese weighs 5 lb. Can the jar of jam that completes the package
weigh 7 lb?
Variables and EquationsVariables and Equations
Lesson 2-4
9 + 5 + j = 20
Equation 5 + =j 20
weight of cheese
Words plus
= weight of jam.
is 20 lbweight of
jam
9
j
weight of apples plus
Let
+
14 + j = 20 Add.
14 + 7 20 Substitute 7 for the variable.
No, the jar of jam cannot weigh 7 lb.
21 20 =/ Quick Check
Additional Examples
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Variables and EquationsVariables and Equations
Lesson 2-4
1. Is b + 3b – 1 = 15 true, false, or an open sentence?
2. Write an equation for A number added to seven times the number is the opposite of thirty-two. Is the equation true, false, or an open sentence?
3. Is 25 a solution of the equation 175 – x = 150?
4. Can you stack eight books that are each 3 in. thick inside a box that is 18 in. tall?
yes
open sentence
7x + x = –32; open sentence
no
Lesson Quiz
2-4
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
Lauralee pitched 12 innings. Maureen pitched 3 fewer innings.How many innings did Maureen pitch?
23
8 13
Problem of the Day
2-5
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
(For help, go to Lesson 2-1.)
Simplify each expression.
1. 3 + 4 – 4 2. 7 + 9 – 7
3. 8 – 2 + 2 4. 6 + 2 – 2
Check Skills You’ll Need
Check Skills You’ll Need
2-5
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
Solutions
1. 3 + 4 – 4 2. 7 + 9 – 7 = 3 + (4 – 4) = 9 + (7 – 7)= 3 + 0 = 9 + 0= 3 = 9
3. 8 – 2 + 2 4. 6 + 2 – 2 = 8 + (2 – 2) = 6 + (2 – 2)= 8 + 0 = 6 + 0= 8 = 6
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve y + 5 = 13.
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
Method 1: Method 2:
y + 5 = 13 Subtract 5
y + 5 – 5 = 13 – 5 from each side.
y = 8 Simplify.
y + 5 = 13
y = 8
Check: y + 5 = 13
8 + 5 13 Replace y with 8.
13 = 13
– 5 = – 5
Quick Check
Additional Examples
2-5
![Page 40: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/40.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Larissa wants to increase the number of books in her
collection to 327 books. She has 250 books now. Find the number
of books she needs to buy.
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
target numberWords plusis 250 number to buy
= number to buy.xLet
Equation 327 + x250=
Additional Examples
2-5
![Page 41: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/41.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
(continued)
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
327 = 250 + x
Larissa needs to buy 77 more books.
327 = x + 250 Use the Commutative Property of Addition.
327 – 250 = x + 250 – 250 Subtract 250 from each side.
77 = x Simplify.
Check: Is the answer reasonable?250 plus the number of books bought should be a total collection of 327.
250 + 77 = 327Quick Check
Additional Examples
2-5
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve c – 23 = – 40.
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
c – 23 = – 40
c – 23 + 23 = – 40 + 23 Add 23 to each side.
c = –17 Simplify.
Quick Check
Additional Examples
2-5
![Page 43: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/43.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Marcy’s CD player cost $115 less than her DVD player. Her
CD player cost $78. How much did her DVD player cost?
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
78 = t – 115 Write an equation.
78 + 115 = t – 115 + 115 Add 115 to each side.
193 = t Simplify.
Marcy’s DVD player cost $193.
cost of CD player $115 cost of DVD playerWords less thanwas
t = cost of the DVD player.Let
t 115Equation 78 = –
Quick Check
Additional Examples
2-5
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Adding or SubtractingSolving Equations by Adding or Subtracting
Lesson 2-5
Solve each equation.
1. y + 8 = 12 2. 7 + f – 21 = –20
3. 67 = g – (–36)
4. Ricky rides his bike 12 miles every day. He stops after 7 miles to rest. How much farther does he have to ride?
5 mi
4 –6
31
Lesson Quiz
2-5
![Page 45: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/45.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
0.59521.6
Divide. Round each quotient to the nearest hundredth.
a. b. 10.51262.1
0.372, which rounds to 0.37 5.006, which rounds to 5.01
Problem of the Day
2-6
![Page 46: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/46.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
(For help, go to Lesson 19.)
Simplify each quotient.
1. 2.
3. 4.
1818
21–21
–77
–13–13
Check Skills You’ll Need
Check Skills You’ll Need
2-6
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
Solutions
1. = 1 2. = –1
3. = –1 4. = 1
1818
21–21
–77
–13–13
Check Skills You’ll Need
2-6
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
288 pens are boxed by the dozen. How many boxes
are needed?
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
Let
Equation 288
=
b
number of pensWords times
number of boxes.b
is 12
12
number of boxes
= •
Additional Examples
2-6
![Page 49: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/49.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
(continued)
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
288 = 12b
24 = b Simplify.
24 boxes are needed.
Divide each side by 12.28812
12b12
=
Check: Is the answer reasonable? Twelve times the number of boxes is the number of pens.
Since 12 24 = 288, the answer is reasonable.
Quick Check
Additional Examples
2-6
![Page 50: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/50.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve –2v = –24.
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
–2v = –24
v = 12 Simplify.
Divide each side by –2.–2v–2
–24–2
=
Check: –2v = –24–2 • (12) –24 Replace v with 12.
–24 = –24
Quick Check
Additional Examples
2-6
![Page 51: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/51.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve = – 5.
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
x = – 40 Simplify.
x8
= – 5x8x8
8 = 8(–5) Multiply each side by 8.
Quick Check
Additional Examples
2-6
![Page 52: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/52.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving Equations by Multiplying or DividingSolving Equations by Multiplying or Dividing
Lesson 2-6
–6
Solve each equation.
1. 8x = –48 2. –2x = 18
3. 108 = 9x 4. = 14
5. –6 =
v–3
n4
–9
12 –42
–24
Lesson Quiz
2-6
![Page 53: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/53.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
Find three different odd numbers whose sum is 21. List all possibilities.
1, 3, 17; 1, 5, 15; 1, 7, 13; 1, 9, 11; 3, 5, 13; 3, 7, 11; 5, 7, 9
Problem of the Day
2-7
![Page 54: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/54.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
(For help, go to Lesson 15.)
Simplify.
1. 158 + 20 2. 158 + 30
3. 158 + 25 4. 158 + 22
5. In Exercises 1–4, which result came closest to 181?
Check Skills You’ll Need
Check Skills You’ll Need
2-7
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
Solutions
1. 158 + 20 = 178 2. 158 + 30 = 188
3. 158 + 25 = 183 4. 158 + 22 = 180
5. |181 – 178| = |3| = 3 |181 – 188| = |–7| = 7
|181 – 183| = |–2| = 2 |181 – 180| = |1| = 1
The result of Exercise 4, 180, is the closest to 181.
Check Skills You’ll Need
2-7
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
During the intermission of the play, the Theater Club sold cups
of popcorn and soda. The club sold 79 cups of popcorn and 96 sodas for
a total of $271. What was the selling price of a cup of popcorn? Of a
soda?
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
You can organize conjectures in a table. As a first conjecture, try both with a price of $1.
Additional Examples
2-7
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
(continued)
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
Popcorn SodaPrice Price Total Price
$1 $1 79(1) + 96(1) = 79 + 96 The total is too low. Increase = 175 the price of the popcorn only.
$2 $1 79(2) + 96(1) = 158 + 96 The total is too low. = 254 Increase the price of the soda.
$2 $2 79(2) + 96(2) = 158 + 192 The total is too high. = 350 Decrease the price of the popcorn.
$1 $2 79(1) + 96(2) = 79 + 192 The total is correct. = 271
The popcorn price was $1, and the soda price was $2. Quick Check
Additional Examples
2-7
![Page 58: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/58.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Problem Solving Strategy: Guess, Check, ReviseProblem Solving Strategy: Guess, Check, Revise
Lesson 2-7
Solve using any strategy.
1. A sporting goods store manager ordered twice as many pairs of basketball shoes as tennis shoes. He ordered 96 pairs in all. How many pairs of each did he order?
2. Manuel wrote a 512-word paper over the weekend. He wrote 180 more words on Sunday than he did on Saturday. How many words
did he write on Saturday?166
32 pairs of tennis shoes; 64 pairs of basketball shoes
Lesson Quiz
2-7
![Page 59: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/59.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
Order from least to greatest: , 0.25, , – 0.5, 0.3,– 212
16
–2, – 0.5, , 0.25, 0.3, 12
16
Problem of the Day
2-8
![Page 60: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/60.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
(For help, go to Lesson 14.)
Graph each set of numbers on a number line. Order the numbers from least to greatest.
1. –3, 7, –9 2. –2, –10, –8
3. 0, 3, –5 4. 3, –6, 10
Check Skills You’ll Need
Check Skills You’ll Need
2-8
![Page 61: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/61.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
Solutions
1. –9, –3, 7
2. –10, –8, –2
3. –5, 0, 3
4. –6, 3, 10
Check Skills You’ll Need
2-8
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
An open dot shows that –2 is not a solution.
A closed dot shows that –5 is a solution.
Shade all the points to the right of –5.
Shade all the points to the right of –2.
Graph the solutions of each inequality on a number
line.
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
a. x > –2
b. w –5 >–
Additional Examples
2-8
![Page 63: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/63.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
(continued)
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
c. k 4
d. y < 6
<– A closed dot shows that 4 is a solution.
Shade all the points to the left of 4.
An open dot shows that 6 is not a solution.
Shade all the points to the left of 6. Quick Check
Additional Examples
2-8
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Write the inequality shown in each graph.
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
a.
b.
x –3 >–
x < 3
Quick Check
Additional Examples
2-8
![Page 65: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/65.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Food can be labeled very low sodium only if it meets the requirement established by the federal government. Use the table to write an inequality for this requirement.
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
Label Definition
Sodium-free food Less than 5 mg per serving
Very low sodium food At most 35 mg per serving
Low-sodium food At most 140 mg per serving
Additional Examples
2-8
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
(continued)
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
=
35 mg sodiumWords
number of milligrams of sodium in a serving ofvery low sodium food.
v
has at mosta serving of very low sodium food
Let
Inequality 35v <–
Quick Check
Additional Examples
2-8
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Inequalities and Their GraphsInequalities and Their Graphs
Lesson 2-8
x > –30
1. Graph –7 w.
2. Write an inequality for the graph.
3. A child must be at least 50 in. tall to ride on the roller coaster. Write an inequality for this situation.
>–
h 50>–
Lesson Quiz
2-8
![Page 68: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/68.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Lesson 2-9
Solve each equation.
a. n + 4 = 3 b. 4 – p = 8
n = –1 p = – 4
Problem of the Day
2-9
![Page 69: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/69.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-9
(For help, go to Lesson 2-5.)
Solve each equation.
1. m + 7 = 5 2. k – 8 = 11
3. 12 + h = 21 4. 6 = n – 23
Check Skills You’ll Need
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Check Skills You’ll Need
2-9
![Page 70: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/70.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-9
Solutions
1. 2. m + 7 – 7 = 5 – 7 k – 8 + 8 = 11 + 8
3. 4.12 – 12 + h = 21 – 12
m + 7 = 5
m = – 2
12 + h = 21
h = 9
6 = n – 23
29 = n6 + 23 = n – 23 + 23
k – 8 = 11
k = 19
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Check Skills You’ll Need
2-9
![Page 71: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/71.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve each inequality. Graph the solutions.
Lesson 2-9
a.
b.
4 + s – 4 < 12 – 4 Subtract 4 from each side.
4 + s < 12
s < 8 Simplify.
4 + s < 12
–16 y – 14 >––16 y – 14 > –
–16 + 14 y – 14 + 14 Add 14 to each side.>– –2 y or y –2 Simplify.>– <–
Quick Check
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Additional Examples
2-9
![Page 72: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/72.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Suppose your computer’s hard drive has a capacity of 6
gigabytes (GB). The files you have stored on the hard drive occupy
at least 2 GB. How much storage space is left for other files?
Lesson 2-9
= storage space available.sLet
storage space for our filesWords
is less than or equal toplus
totalspace
storage space left
Inequality 2 s 6+ <–
2 + s 6<–
2 – 2 + s 6 – 2 Subtract 2 from each side.<–
s 4 Simplify.<–
At most 4 GB are left.
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Quick Check
Additional Examples
2-9
![Page 73: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/73.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solve –10 < –13 + q.
Lesson 2-9
–10 < –13 + q
–10 + 13 < –13 + 13 + q Add 13 to each side.
3 < q Simplify.
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Quick Check
Additional Examples
2-9
![Page 74: FeatureLesson Pre-Algebra Lesson Main Properties of Numbers Lesson 2-1 At the Red Valley Sports Camp, 15 kids went horseback riding, 14 played tennis,](https://reader035.vdocuments.net/reader035/viewer/2022062310/56649e265503460f94b155ee/html5/thumbnails/74.jpg)
FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-9
Solve each inequality.
1. e + 4 14 2. –22 g – 6
3. A number q plus the opposite of 5 is less than or equal to 0.
>–<––16 g>–e 10<–
q 5<–
Solving One-Step Inequalities by Adding or SubtractingSolving One-Step Inequalities by Adding or Subtracting
Lesson Quiz
2-9
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Lesson 2-10
Solve each equation.
a. q ÷ 3 = 6 b. 7r = 21
q = 18 r = 3
Problem of the Day
2-10
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-10
(For help, go to Lesson 2-6.)
Solve each equation.
1. 6x = 24 2. 63 = –7v
3. = 10 4. = 48 t6
x–2
Check Skills You’ll Need
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Check Skills You’ll Need
2-10
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-10
Solutions
1. 2.
3. 4.
–2 = –2(10)
6x = 24
x = 4
= 10
x = –20
= 48
t = 288
6 = 48(6)
63 = –7v
–9 = v
x–2
6x6
246
63–7
–7v–7
x–2
==
t6
t6
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Check Skills You’ll Need
2-10
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-10
A 1-ton truck has the ability to haul 1 ton, or 2,000 lb.
At most, how many television sets can the truck carry if each
TV set weighs 225 lb?
225x 2,000<–
Let x = number of televisions.
Inequality
Wordsnumber oftelevisions
225 lb 2,000 lbtimesis less thanor equal to
x • 225 2,000<–
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Additional Examples
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-10
(continued)
Divide each side by 225.<–2,000225
225x225
x 8.8 Simplify. Round the answer down to find a wholenumber of television sets.
<–
At most, the truck can carry 8 television sets.
Check: Is the answer reasonable? The total weight of 8 television sets is 8(225) = 1,800 lb, which is less than 2,000 lb but so close that another television set could not be carried. The answer is reasonable.
Quick Check
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Additional Examples
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
Lesson 2-10
Solve –2.z–8
<–
–2z
–8<–
Multiply each side by –8 and reverse the inequality symbol.
–8(–2)z
–8–8 >–
Simplify.z 16>–
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Quick Check
Additional Examples
2-10
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FeatureLesson
Pre-AlgebraPre-Algebra
LessonMain
>–
Solve each inequality.
1. 3x –27 2. –5w > 15
3. y 4. 0
5. 4f > –12
–x5
<–14
12
<–
Lesson 2-10
w < –3
x 0>–
x –9>–
f > –3
y 2<–
Solving One-Step Inequalities by Multiplying or DividingSolving One-Step Inequalities by Multiplying or Dividing
Lesson Quiz
2-10