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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

1-2

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

1-2

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.

1-2

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.

1-2

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.

1-2

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.

1-2

Exponents and Order of Operations

ALGEBRA 1 LESSON 1-2

Evaluate each expression for x 11 and z 16.

a. (xz)2

b. xz2

1-2

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.

1-2

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.

1-2

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

1-2

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

1-3

Exploring Real Numbers

ALGEBRA 1 LESSON 1-3

1-3

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

1-3

Exploring Real Numbers

ALGEBRA 1 LESSON 1-3

Which set of numbers is most reasonable for

displaying outdoor temperatures?

integers

1-3

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.

1-3

Exploring Real Numbers

ALGEBRA 1 LESSON 1-3

Write , , and , in order from

least to greatest.

1-3

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

1-3

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

1-3

Multiplying and Dividing Real Numbers

ALGEBRA 1 LESSON 1-6

Evaluate 4z2 for x 4, y 2, and z

4.

1-6

Multiplying and Dividing Real Numbers

ALGEBRA 1 LESSON 1-6

Evaluate for p and r .

2 Simplify.

1-6

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

1-6

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)

1-7

The Distributive Property

ALGEBRA 1 LESSON 1-7

1-7

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

1-7

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.

1-7

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.

1-7

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.

1-7

The Distributive Property

ALGEBRA 1 LESSON 1-7

Simplify 2w2 w2.

2w2 w2 (2 1)w2 Use the Distributive

Property.

w2 Simplify.

1-7

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)

1-7

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

1-7

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

1-8

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

1-8

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

1-8

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.

1-8

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

1-8

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

1-8

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