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

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 *You must group when you are adding more than 2 items Inverse property of addition b. 8.3 + (– 8.3) = 0 *Adding a number and its’ opposite equals zero c. – y + 0.7 = 0.7 + (– y) Commutative property of addition *You can add in any order

EXAMPLE 2: Add Real Numbers Find the sum. a. – 5.3 + (– 4.9) = – ( – 5.3 + – 4.9 ) Rule of same signs = – (5.3 + 4.9) Take absolute values. = – 10.2 Add. b. 19.3 + (–12.2) Rule of different signs = 19.3 – –12.2 = 19.3 – 12.2 Take absolute values. = 7.1 Subtract.

GUIDED PRACTICE 1. – 0.6 + (– 6.7) Rule of same signs Find the sum. 1. – 0.6 + (– 6.7) = – (| – 0.6 | + | – 6.7| ) Rule of same signs = – (0.6 + 6.7) Take absolute values. = – 7.3 Add. Find the sum. 2. 10.1 + (– 16.2) = – ( |10.1| + |– 16.2| ) Rule of different signs = 10.1 – 16.2 Take absolute values. = – 6.1 Subtract.

GUIDED PRACTICE 1. 7 + (– 7) = 0 Inverse property of addition Find the sum. 3. – 13.1 + 8.7 = – |– 13.1 | + |8.7| Rule of different signs = – 13.1 + 8.7 Take absolute values. = – 4.4 Subtract. 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

EXAMPLE 1: Subtract Real Numbers Find the difference. a. – 12 – 19 = – 12 + (– 19) = – 31 b. 18 – (–7) = 18 + 7 = 25

GUIDED PRACTICE Find the difference. 1. – 2 – 7 = – 2 + (– 7) = – 9 1. – 2 – 7 = – 2 + (– 7) = – 9 2. 11.7– (– 5) = 11.7 + 5 = 16.7 3. -

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

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 – 5.2 + 8 = – 0.2 2. y – (x – 2) = 5.2 – (– 3 – 2) = 5.2 – (– 5 ) = 5.2 + 5 = 10.2

GUIDED PRACTICE 3. (y – 4) – x = (5.2 – 4) – (– 3) = 1.2 + 3 = 4.2

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

EXAMPLE 1 Multiply real numbers Find the product. a. – 3 (6) = – 18 Different signs; product is negative. a. – 3 (6) = – 18 b. 2 (–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.

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. (–3) (7) 4 3 = – 4 (7) Multiply and – 3. 4 3 = – 28 Different signs; product is negative.

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. 8 · 0 = Multiplicative property of zero c. – 6 · y = y · (– 6) Commutative property of multiplication d. 9 · (– 1) = – 9 Multiplicative property of – 1 e. 1 · v = v Identity property of multiplication

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

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. ·

EXAMPLE 2 Divide real numbers Find the quotient. a. –16 4 = –4 –20 b. 5 3 – = –20 ·(-3/5) = 12

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 –

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 ·

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 = –

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

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.

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.

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

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