Find each product. 1.4 42.7 73.5 54.9 9 Perform the indicated operations. 5.3 + 12 – 76.6 1 ÷ 2 7.4 – 2 + 98.10 – 5 – 4 9.5 5 + 710. 30 ÷ 6 2 ALGEBRA 1

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

ALGEBRA 1 LESSON 1-2ALGEBRA 1 LESSON 1-2

Exponents and Order of OperationsExponents and Order of Operations

1-2

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



Solutions

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

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

Find the total cost of a pair of jeans that cost $32 and have

an 8% sales tax.

total cost original price sales taxC = p + r • p

sales tax rate

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

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

Evaluate each expression for x = 11 and z = 16.

a. (xz)2

= (176)2 Simplify within parentheses. Multiply. = 11 • 256

= 2816= 30,976 Simplify.

(xz)2 = (11 • 16)2 Substitute 11 for x and 16 for z. xz2 = 11 • 162



1-2

b. xz2

Simplify 4[(2 • 9) + (15 ÷ 3)2].

4[(2 • 9) + (15 ÷ 3)2] = 4[18 + (5)2] First simplify (2 • 9) and (15 ÷ 3).

= 4[18 + 25] Simplify the power.

= 4[43] Add within brackets.

= 172 Multiply.



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.

= 3(261) Simplify the fraction.

= 783 Multiply.

The total area of all three decks is 783 ft2.

A = 3 ( )pa2

= 3 ( ) 60 • 8.7

2Substitute 60 for p and 8.7 for a.

= 3 ( )5222

Simplify the numerator.



1-2

Use the formula A = 3 ( ) to find the total area of all three decks.pa2


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

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

(For help, go to skills handbook page 725.)


Exploring Real NumbersExploring Real Numbers

1-3

25

38

23

59



1-3

1. 0.5 = = =

2. 0.05 = = =

3. 3.25 = 3 = 3 = 3 or

4. 0.325 = = =

5. = 2 ÷ 5 = 0.4

6. = 3 ÷ 8 = 0.375

7. = 2 ÷ 3 = 0.6

8. 3 = 3 + (5 ÷ 9) = 3.5

5 10

12

5 • 15 • 2

5 100

5 • 1 5 • 20

25 100

14

134

25 • 125 • 4

325 1000

25 • 1325 • 40

1340

25

38

23

59

Solutions

1 20

Name the set(s) of numbers to which each number belongs.

a. –13 b. 3.28

integers

rational numbers

rational numbers



1-3

Which set of numbers is most reasonable for displaying

outdoor temperatures?

integers



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.

A negative number can be a fraction, such as – . This is not an integer.23



1-3

Write – , – , and – , in order from least to greatest.

– = –0.75 Write each fraction as a decimal.

– = –0.583

– = –0.625

34

7 12

58

From least to greatest, the fractions are – , – , and – .34

7 12

58

–0.75 < –0.625 < –0.583 Order the decimals from least to greatest.



1-3

34

7 12

58

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


Name the set(s) of numbers to which each given number belongs.

1. –2.7 2. 11 3. 16

Use <, =, or > to compare.

4. 5.

6. Find |– |.

34

58

rational numbers irrational numbers natural numbers, whole numbersintegers, rational numbers

– –

7 12

> <

7 12


1-3

34

58

Evaluate – – 4z2 for x = 4, y = –2, and z = –4.

– – 4z2 = – 4(–4)2 Substitute 4 for x, –2 for y, and –4 for z.xy

–4–2

= – 4(16) Simplify the power.–4–2

= 2 – 64 Divide and multiply.

= –62 Subtract.


Multiplying and Dividing Real NumbersMultiplying and Dividing Real Numbers

1-6

xy

Evaluate for p = and r = – .

= –2 Simplify.

= p ÷ r Rewrite the equation.pr

= ÷ Substitute for p and – for r.32

34

(– ) 32

34

= Multiply by – , the reciprocal of – .32

43(– ) 4

334



1-6

pr

32

34


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 = – .

56 – 22

–7 27 12

312


1-6

8mn

13

12


(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)

The Distributive PropertyThe Distributive Property

1-7

12



1-7

( )

1. 3(4 + 7) = 3(11) = 33

2. –2(5 + 6) = –2(11) = –22

3. –1(–9 + 8) = –1(–1) = 1

4. –0.5(8 – 6) = –0.5(2) = –1

5. t(10 – 4) = t(6) = (6)t = • 6 t = 3t

6. m(–3 – 1) = m(–4) = –4m

12

12

12

12

Solutions

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

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.

= 52 – 0.04 Simplify.

= 51.96

The total cost of 4 CDs is $51.96.



1-7

Simplify 3(4m – 7).

3(4m – 7) = 3(4m) – 3(7) Use the Distributive Property.

= 12m – 21 Simplify.



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

Simplify –2w2 + w2.

–2w2 + w2 = (–2 + 1)w2 Use the Distributive Property.

= –w2 Simplify.



1-7

Relate: –6 times the quantity 7 minus m

Write: –6 • (7 – m)

Write an expression for the product of –6 and the quantity 7

minus m.

–6(7 – m)



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

47

35b –( )


1-7

47

35


(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

Properties of Real NumbersProperties of Real Numbers

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

Name the property each equation illustrates.

a. 3 • a = a • 3

b. p • 0 = 0

c. 6 + (–6) = 0



1-8

Commutative Property of Multiplication, because the order of the factors changes

Multiplication Property of Zero, because a factor multiplied by zero is zero

Inverse Property of Addition, because the sum of a number and its inverse is zero

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

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


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

Documents

Find each product. 1.4 42.7 73.5 54.9 9 Perform the indicated operations. 5.3 + 12 – 76.6 1 ÷ 2 7.4 – 2 + 98.10 – 5 – 4 9.5 5 + 710. 30 ÷ 6 2 ALGEBRA 1