Exponents and Order of Operations

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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Find each product. 1. 4 4 2. 7 7 3. 5
5 4. 9 9 Perform the indicated
operations. 5. 3 12 7 6. 6 1 2 7. 4
2 9 8. 10 5 4 9. 5 5 7 10. 30 6
2
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Solutions
1. 4 4 16 2. 7 7 49 3. 5 5
25 4. 9 9 81 5. 3 12 7 (3 12) 7
15 7 8 6. 6 1 2 (6 1) 2 6 2
3 7. 4 2 9 (4 2) 9 2 9 11 8. 10
5 4 (10 5) 4 5 4 1 9. 5 5 7
(5 5) 7 25 7 32 10. 30 6 2 (30
6) 2 5 2 10
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Simplify 32 62 14 3.
32 62 14 3 32 36 14 3 Simplify the
power 62 6 6 36.
32 36 42 Multiply 14 and 3.
68 42 Add and subtract in order from left to
right.
26 Subtract.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Evaluate 5x 32 p for x 2 and p 3.
5x 32 p 5 2 32 3 Substitute 2 for x
and 3 for p.
5 2 9 3 Simplify the power.
10 3 Multiply and divide from left to right.
13 Add.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Find the total cost of a pair of jeans that cost
32 and have an 8 sales tax.
C p r p 32 0.08 32 Substitute 32 for
p. Change 8 to 0.08 and substitute 0.08 for r.
32 2.56 Multiply first.
34.56 Then add.
The total cost of the jeans is 34.56.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Simplify 3(8 6) (42 10).
3(8 6) (42 10) 3(8 6) (16
10) Simplify the power.
3(14) 6 Simplify within parentheses.
42 6 Multiply and divide from left to right.
7 Divide.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Evaluate each expression for x 11 and z 16.
a. (xz)2
b. xz2
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Simplify 4(2 9) (15 3)2.
4(2 9) (15 3)2 418 (5)2 First
simplify (2 9) and (15 3).
418 25 Simplify the power.
443 Add within brackets.
172 Multiply.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
A carpenter wants to build three decks in the
shape of regular hexagons. The perimeter p of
each deck will be 60 ft. The perpendicular
distance a from the center of each deck to one of
the sides will be 8.7 ft.
The total area of all three decks is 783 ft2.
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Exponents and Order of Operations
ALGEBRA 1 LESSON 1-2
Simplify each expression. 1. 50 4 3
6 2. 3(6 22) 5 3. 2(1 5)2 (18
3) Evaluate each expression. 4. 4x 3y for x
2 and y 4 5. 2 p2 3s for p 3 and s
11 6. xy2 z for x 3, y 6 and z 4
44
25
60
20
51
112
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
(For help, go to skills handbook page 725.)
Write each decimal as a fraction and each
fraction as a decimal. 1. 0.5 2. 0.05 3. 3.25 4.
0.325 5. 6. 7. 8. 3
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Name the set(s) of numbers to which each number
belongs.
a. 13
b. 3.28
integers
rational numbers
rational numbers
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Which set of numbers is most reasonable for
displaying outdoor temperatures?
integers
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Determine whether the statement is true or
false. If it is false, give a counterexample.
All negative numbers are integers.
The statement is false.
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Write , , and , in order from
least to greatest.
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Find each absolute value.
a. 2.5
b. 7
2.5 is 2.5 units from 0 on a number line.
7 is 7 units from 0 on a number line.
2.5 2.5
7 7
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Exploring Real Numbers
ALGEBRA 1 LESSON 1-3
Name the set(s) of numbers to which each given
number belongs. 1. 2.7 2. 11 3. 16 Use lt,
, or gt to compare. 4. 5. 6. Find .
rational numbers
irrational numbers
natural numbers, whole numbers integers,
rational numbers
3 4
5 8
gt
lt


7 12
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Multiplying and Dividing Real Numbers
ALGEBRA 1 LESSON 1-6
Evaluate 4z2 for x 4, y 2, and z
4.
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Multiplying and Dividing Real Numbers
ALGEBRA 1 LESSON 1-6
Evaluate for p and r .
2 Simplify.
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Multiplying and Dividing Real Numbers
ALGEBRA 1 LESSON 1-6
Simplify. 1. 8(7) 2. 6(7 10)
4 Evaluate each expression for m 3, n 4,
and p 1. 3. p 4. (mp)3 5.
mnp 6. Evaluate 2a 4b c for a 2, b
, and c .
22
56
7
27
12
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The Distributive Property
ALGEBRA 1 LESSON 1-7
(For help, go to Lessons 1-2 and 1-6.)
Use the order of operations to simplify each
expression. 1. 3(4 7) 2. 2(5 6) 3. 1(9
8) 4. 0.5(8 6) 5. t(10 4) 6. m(3 1)
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The Distributive Property
ALGEBRA 1 LESSON 1-7
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Use the Distributive Property to simplify 26(98).
26(98) 26(100 2) Rewrite 98 as 100 2.
26(100) 26(2) Use the Distributive Property.
2600 52 Simplify.
2548
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Find the total cost of 4 CDs that cost 12.99
each.
4(12.99) 4(13 0.01) Rewrite 12.99 as 13
0.01.
4(13) 4(0.01) Use the Distributive Property.
The total cost of 4 CDs is 51.96.
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Simplify 3(4m 7).
3(4m 7) 3(4m) 3(7) Use the Distributive
Property.
12m 21 Simplify.
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Simplify (5q 6).
(5q 6) 1(5q 6) Rewrite the expression
using 1.
1(5q) 1(6) Use the Distributive Property.
5q 6 Simplify.
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Simplify 2w2 w2.
2w2 w2 (2 1)w2 Use the Distributive
Property.
w2 Simplify.
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Write an expression for the product of 6 and
the quantity 7 minus m.
6(7 m)
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The Distributive Property
ALGEBRA 1 LESSON 1-7
Simplify each expression. 1. 11(299) 2.
4(x 8) 3. 3(2y 7) 4. (6 p)
5. 1.3a 2b 4c 3.1b 4a 6. Write an
expression for the product of and the quantity
b minus .
3289
4x 32
6y 21
6 p
2.7a 5.1b 4c
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
(For help, go to Lessons 1-4 and 1-6.)
Simplify each expression. 1. 8 (9 2) 2. 3
(2 5) 3. 7 16 3 4. 4(7)(5) 5. 6 9
(4) 6. 0.25 3 4 7. 3 x 2 8. 2t 8
3t 9. 5m 2m 4m
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
1. 8 (9 2) 8 (2 9) (8 2) 9
10 9 19 2. 3 (2 5) 3 (10) 30 3.
7 16 3 7 3 16 10 16 26 4.
4(7)(5) 4(5)(7) 20(7) 140 5. 6 9
(4) 6 (4) 9 10 9 1 6. 0.25 3
4 0.25 4 3 1 3 3 7. 3 x 2 3
(2) x 1 x 8. 2t 8 3t 2t 3t 8
(2 3)t 8 5t 8 9. 5m 2m 4m (5
2 4)m 7m
Solutions
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
Name the property each equation illustrates.
a. 3 a a 3
Commutative Property of Multiplication, because
the order of the factors changes
b. p 0 0
Multiplication Property of Zero, because a factor
multiplied by zero is zero
c. 6 (6) 0
Inverse Property of Addition, because the sum of
a number and its inverse is zero
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
Suppose you buy a shirt for 14.85, a pair of
pants for 21.95, and a pair of shoes for 25.15.
Find the total amount you spent.
14.85 21.95 25.15 14.85 25.15
21.95 Commutative Property of Addition
(14.85 25.15) 21.95 Associative Property of
Addition
40.00 21.95 Add within parentheses first.
61.95 Simplify.
The total amount spent was 61.95.
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
Simplify 3x 4(x 8). Justify each step.
3x 4(x 8) 3x 4x 32 Distributive Property
(3 4)x 32 Distributive Property
1x 32 Subtraction
x 32 Identity Property of Multiplication
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Properties of Real Numbers
ALGEBRA 1 LESSON 1-8
Name the property that each equation
illustrates. 1. 1m m 2. ( 3 4) 5 3
(4 5) 3. 14 0 0 4. Give a reason to
justify each step.
Iden. Prop. Of Mult.
Assoc. Prop. Of Add.
Mult. Prop. Of Zero
a. 3x 2(x 5) 3x 2x 10
Distributive Property
b. 3x ( 2x) ( 10)
Definition of Subtraction
c. 3 ( 2)x ( 10)
Distributive Property
d. 1x ( 10)
Addition
e. 1x 10
Definition of Subtraction
f. x 10
Identity Property of Multiplication
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