1. Operations: Add, Subtract, Multiply, Divide
Algebra 1
Operations:
Add, Subtract, Multiply, Divide

2. Vocabulary Additive Identity: the number 0 (in the identity property)
Additive Inverse:
the number’s opposite
(in the inverse property)

3. EXAMPLE 3: Identify Properties of Addition
Statement
Property illustrated
a. (x + 9) + 2 = x + (9 + 2)
Associative property of addition
*You must group when you are adding more than 2 items
Inverse property of addition
b (– 8.3) = 0
*Adding a number and its’ opposite equals zero
c. – y = (– y)
Commutative property of addition
*You can add in any order

4. EXAMPLE 2: Add Real Numbers
Find the sum.
a. – (– 4.9)
= – ( – – 4.9 )
Rule of same signs
= – ( )
Take absolute values.
= – 10.2
Add.
b (–12.2)
Rule of different signs
= – –12.2
= 19.3 – 12.2
Take absolute values.
= 7.1
Subtract.

5. GUIDED PRACTICE 1. – 0.6 + (– 6.7) Rule of same signs
Find the sum.
1. – (– 6.7)
= – (| – 0.6 | + | – 6.7| )
Rule of same signs
= – ( )
Take absolute values.
= – 7.3
Add.
Find the sum.
(– 16.2)
= – ( |10.1| + |– 16.2| )
Rule of different signs
= 10.1 – 16.2
Take absolute values.
= – 6.1
Subtract.

6. GUIDED PRACTICE 1. 7 + (– 7) = 0 Inverse property of addition
Find the sum.
3. –
= – |– 13.1 | + |8.7|
Rule of different signs
= –
Take absolute values.
= – 4.4
Subtract.
Identify the property being illustrated.
(– 7) = 0
Inverse property of addition
2. – = – 12
Identity property of addition
= 8 + 4
Commutative property of addition

7. EXAMPLE 1: Subtract Real Numbers
Find the difference.
a. – 12 – 19
= – 12 + (– 19)
= – 31
b – (–7) =
= 25

8. GUIDED PRACTICE Find the difference. 1. – 2 – 7 = – 2 + (– 7) = – 9
1. – 2 – 7
= – 2 + (– 7)
= – 9
– (– 5) =
= 16.7 3. -

9. EXAMPLE 2: Evaluate a Variable Expression
Evaluate the expression y – x when x = – 2 and y = 7.2
y – x =
7.2– (–2) + 6.8
Substitute – 2 for x and 7.2 for y. =
Add the opposite – 2.
= 16
Add.

10. GUIDED PRACTICE x – y + 8 = – 3 – (5.2) + 8 = – 3 – 5.2 + 8 = – 0.2
Evaluate the expression when x = – 3 and y = 5.2. 1.
x – y + 8
= – 3 – (5.2) + 8
= – 3 –
= – 0.2 2.
y – (x – 2)
= 5.2 – (– 3 – 2)
= 5.2 – (– 5 ) =
= 10.2

11. GUIDED PRACTICE 3.
(y – 4) – x
= (5.2 – 4) – (– 3) =
= 4.2

12. Vocabulary
Multiplicative Inverse: 1/a; the reciprocal of a number a so that when they are multiplied the product is 1

13. EXAMPLE 1 Multiply real numbers Find the product. a. – 3 (6) = – 18
Different signs; product is
negative.
a. – 3 (6)
= – 18
b (–5) (–4)
(–10) (–4) =
Multiply 2 and – 5.
Same signs; product is
positive.
= 40
Multiply – and – 4 1 2
c. – (–4) (–3) 1 2
= 2 (– 3)
= – 6
Different signs; product is
negative.

14. GUIDED PRACTICE Find the product. 1. – 2 (– 7) = (– 2) (– 7) = 14
1. – 2 (– 7)
= (– 2) (– 7)
= 14
Same signs; product is positive.
2. – 0.5 (– 4) (– 9)
= (2) (– 9)
Multiply – 0.5 and – 4.
= – 18
Different signs; product is negative.
(–3) (7) 4 3
= – 4 (7)
Multiply and – 3. 4 3
= – 28
Different signs; product is
negative.

15. Identify properties of multiplication
EXAMPLE 2
Identify properties of multiplication
Statement
Property illustrated
x · (7 · 0.5)
a. (x · 7) · 0.5 =
Associative property of multiplication
b · 0 =
Multiplicative property of zero
c. – 6 · y =
y · (– 6)
Commutative property of multiplication
d · (– 1) =
– 9
Multiplicative property of – 1
e · v = v
Identity property of multiplication

16. GUIDED PRACTICE Identify the property illustrated. 1. –1 · 8 = – 8
1. –1 · 8 =
– 8
Multiplicative property of – 1
12 · x =
x · 12 2.
Commutative property of multiplication
y · (4 · 9)
(y · 4) · 9 = 3.
Associative property of multiplication 4.
0 · (– 41) = 0
Multiplicative property of zero 5.
– 5 · (– 6) =
– 6 ·
(– 5)
Commutative property of multiplication 6.
13 · (– 1)
– 13 =
Multiplicative property of – 1

17. Find multiplicative inverses of numbers
EXAMPLE 1
Find multiplicative inverses of numbers
a. The multiplicative inverse of 1 5 – is
– 5
because 1 5 –
(– 5)
= 1.
b. The multiplicative inverse of 6 7 – is
because 6 7 –
= 1.

18. EXAMPLE 2
Divide real numbers
Find the quotient. a. – = –4
–20 b. 5 3 – =
–20 ·(-3/5)
= 12

19. GUIDED PRACTICE Find the multiplicative inverse of the number. 1. – 27
1. – 27
The multiplicative inverse of – 27 is 1 27 –
because
= 1.
– 27 1 27 –
2. – 8
The multiplicative inverse of – 8 is 1 8 –
because
= 1.
– 8 1 8 –

20. GUIDED PRACTICE 3. – 4 7 The multiplicative inverse of – is 7 4 –
3. – 4 7
The multiplicative inverse of – is 7 4 –
because
= 1. – 7 4
4. – 1 3
The multiplicative inverse of –
is – 3
because 1 3
– (– 3) = 1 1 3

21. GUIDED PRACTICE 5. – 64 ÷ (– 4) = = 16 6. – 3 8 10 = 10 3 – 8 1 4 = –
5. – 64 ÷ (– 4) =
= 16
6. – 3 8 10 = 10 3 – 8 ÷ 1 4
= –

22. GUIDED PRACTICE 2 9 7. 18 ÷ – = 18 · – 9 2 = – 81 2 1 2 – 8. – ÷ 18 =
÷ – = 2 9
18 · – 9 2
= – 81 2 5
8. – ÷ 18 = – 2 5 1 18 1 45
= –

23. Simplify an expression
EXAMPLE 4
Simplify an expression
Simplify the expression
36x 24 6 – .
36x 24 6 – =
36x 24 – 6 ( ) ÷
Rewrite fraction as division. =
36x 24 – 1 6 ) (
Division rule =
36x 1 6 – 24
Distributive property
6x – 4 =
Simplify.

24. Simplify the expression 2x – 8 – 4 1.
GUIDED PRACTICE
Simplify the expression
2x – 8
– 4 1.
2x – 8
– 4 =
2x 8 – 4 ( ) ÷
Rewrite fraction as division. ) ( =
2x – 8 1 4 –
Division rule = 2x 1 4 – 8
Distributive property
– x = 1 2
+ 2
Simplify.

25. GUIDED PRACTICE – 6y +18 2. 3 – 6y + 18 (– 6y + 18) 3 = 3 1÷
Rewrite fraction as division.
= (– 6y + 18) 1 3
Division rule
= – 6y 1 3
Distributive property
= – 2y + 6
Simplify.

26. GUIDED PRACTICE – 10z – 20 3. – 5 – 10z – 20 (– 10z – 20) – 5 = – 5 1÷
Rewrite fraction as division.
= (– 10z – 20) – 1 5
Division rule
= – 10z – – – 1 5
Distributive property
= 2z + 4
Simplify.