Operations:Add, Subtract, Multiply,

Divide

Algebra 1

Vocabulary Additive Identity:

the number 0 (in the identity property)

Additive Inverse: the number’s opposite

(in the inverse property)

EXAMPLE 3: Identify Properties of Addition

Statement Property illustrated

a. (x + 9) + 2 = x + (9 + 2) Associative property of addition

b. 8.3 + (– 8.3) = 0Inverse property of addition

c. – y + 0.7 = 0.7 + (– y) Commutative property of addition

*You can add in any order

*Adding a number and its’ opposite equals zero

*You must group when you are adding more than 2 items

EXAMPLE 2: Add Real NumbersFind the sum.

Rule of same signs

Take absolute values.= – (5.3 + 4.9)

= – 10.2 Add.

a. – 5.3 + (– 4.9)

Rule of different signs

Take absolute values. = 19.3 – 12.2

= 7.1 Subtract.

b. 19.3 + (–12.2) = 19.3 – –12.2

= – ( – 5.3 + – 4.9 )

Find the sum.

Rule of same signs

Take absolute values.= – (0.6 + 6.7)

= – 7.3 Add.

1. – 0.6 + (– 6.7)

Find the sum.

Take absolute values.

= – 6.1

2. 10.1 + (– 16.2) Rule of different signs

Subtract.

= 10.1 – 16.2

= – (| – 0.6 | + | – 6.7| )

= – ( |10.1| + |– 16.2| )

GUIDED PRACTICE

GUIDED PRACTICEFind the sum.

Take absolute values.= – 13.1 + 8.7

= – 4.4

3. – 13.1 + 8.7 Rule of different signs

Identify the property being illustrated.

1. 7 + (– 7) = 0 Inverse property of addition

2. – 12 + 0 = – 12 Identity property of addition

3. 4 + 8 = 8 + 4 Commutative property of addition

Subtract.

= – |– 13.1 | + |8.7|

= 25

= – 31

Find the difference.

EXAMPLE 1: Subtract Real Numbers

a. – 12 – 19

b. 18 – (–7)

= – 12 + (– 19)

= 18 + 7

= – 9

Find the difference.

1. – 2 – 7 = – 2 + (– 7)

= 16.7

2. 11.7– (– 5) = 11.7 + 5

3.1 1

3 2 1(2) 1(3)

3 2

2 3

6

1

6

GUIDED PRACTICE

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Substitute – 2 for x and 7.2 for y.

Add the opposite – 2.= 7.2 + 2 + 6.8

Evaluate the expression y – x + 6.8 when x = – 2 and y = 7.2

EXAMPLE 2: Evaluate a Variable Expression

y – x + 6.8 =

= 16 Add.

7.2– (–2) + 6.8

Evaluate the expression when x = – 3 and y = 5.2.1. x – y + 8= – 3 – (5.2) + 8

= – 3 – 5.2 + 8

= – 0.22. y – (x – 2)= 5.2 – (– 3 – 2)

= 5.2 – (– 5 )

= 5.2 + 5

= 10.2

GUIDED PRACTICE

GUIDED PRACTICE

3. (y – 4) – x= (5.2 – 4) – (– 3)

= 1.2 + 3

= 4.2

Multiplicative Inverse: 1/a; the reciprocal of a number

a so that when they are multiplied the product is 1

Vocabulary

Different signs; product isnegative.

Same signs; product ispositive.

Multiply 2 and – 5.

Different signs; product isnegative.

Find the product.

EXAMPLE 1

Multiply real numbers

a. – 3 (6)

b. 2 (–5) (–4)

= 40

c. – (–4) (–3)12

Multiply – and – 412

= – 6

= – 18

= 2 (– 3)

(–10) (–4)=

Find the product.

1. – 2 (– 7) = (– 2) (– 7)

Same signs; product is positive.

= 14

2. – 0.5 (– 4) (– 9) = (2) (– 9) Multiply – 0.5 and – 4.

= – 18 Different signs; product is negative.

Different signs; product isnegative.

3. (–3) (7)43

Multiply and – 3.43

= – 28

= – 4 (7)

GUIDED PRACTICE

Multiplicative property of – 1

Identity property of multiplication

Commutative property of multiplication

Associative property of multiplication

Multiplicative property of zero

Property illustratedStatement

EXAMPLE 2

Identify properties of multiplication

x · (7 · 0.5)a. (x · 7) · 0.5 =

b. 8 · 0 = 0

c. – 6 · y =

y · (– 6)

d. 9 · (– 1) =– 9

e. 1 · v =v

Identify the property illustrated.

Multiplicative property of – 1 Commutative property ofmultiplication

Associative property of multiplication

Multiplicative property of zero

Commutative property ofmultiplication

Multiplicative property of – 1

1. –1 · 8 = – 8

12 · x = x · 122.

y · (4 · 9) (y · 4) · 9 =3.

4. 0 · (– 41) = 0

5. – 5 · (– 6) = – 6 · (– 5)

6. 13 · (– 1) – 13=

GUIDED PRACTICE

EXAMPLE 1

Find multiplicative inverses of numbers

a. The multiplicative inverse of15

– is – 5because

b. The multiplicative inverse of67

– is 76

– because

15

– (– 5) = 1.

67

– 76

– = 1.

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·

Find the quotient.

EXAMPLE 2

Divide real numbers

–4

= 12

a. –16 4 =

–20 b. 53

– = –20 ·(-3/5)

Find the multiplicative inverse of the number.

1. – 27

The multiplicative inverse of – 27is 127

– because

= 1.– 27127

–

2. – 8

The multiplicative inverse of – 8is 1 8

– because

= 1. – 8 1 8

–

GUIDED PRACTICE

3. – 47

The multiplicative inverse of – is 7 4

– because47

= 1.– 7 4

–47

4. – 13

The multiplicative inverse of – is – 3 because13

– (– 3) = 113

GUIDED PRACTICE

·

·

= 16

10 3

– 38

14

= –

6. – 38

310

=

5. – 64 ÷ (– 4) =

GUIDED PRACTICE

÷ ·

GUIDED PRACTICE

7. 18 ÷ – =29

18 · – 92

= – 81

25

8. – ÷ 18 = – 25

118

145= –

·

Simplify an expressionEXAMPLE 4

Simplify the expression 36x 24

6

– .

36x 24

6

– Rewrite fraction as division.

Division rule

Distributive property

6x – 4= Simplify.

= 36x 24– 6( )

= 36x 24– 16

)(

= 36x 16

– 16

24

·

· ·

÷

)(= 2x – 8 14

–

GUIDED PRACTICE

Simplify the expression

Rewrite fraction as division.

Division rule

Distributive property

Simplify.

2x – 8

– 4= 2x 8– 4( )

2x – 8

– 41.

= 2x 14

–– 8 14

–

– x= 12 + 2

·

· ·

÷

Rewrite fraction as division.

Division rule

Distributive property

Simplify.

– 6y + 18

3=

– 6y +18

32.

(– 6y + 18) 3

= – 6y + 18 13

13

= – 2y + 6

= (– 6y + 18) 13

GUIDED PRACTICE

÷

·

· ·

Rewrite fraction as division.

Division rule

Distributive property

Simplify.

– 10z – 20

– 5=

– 10z – 20

– 53.

(– 10z – 20) – 5

= 2z + 4

= (– 10z – 20) – 15

= – 10z – – 20 –15

15

GUIDED PRACTICE

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