Algebra 1 Operations Add Subtract Multiply Divide Vocabulary
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 b. 8. 3 + (– 8. 3) = 0 c. – y + 0. 7 = 0. 7 + (– y) Inverse property of addition *Adding a number and its’ opposite equals zero Commutative property of addition *You can add in any order
EXAMPLE 2: Add Real Numbers Find the sum. a. – 5. 3 + (– 4. 9) b. 19. 3 + (– 12. 2) = – ( – 5. 3 + – 4. 9 ) Rule of same signs = – (5. 3 + 4. 9) Take absolute values. = – 10. 2 Add. = 19. 3 – – 12. 2 Rule of different signs = 19. 3 – 12. 2 Take absolute values. = 7. 1 Subtract.
GUIDED PRACTICE 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 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. = – 2 + (– 7) 1. – 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 + 6. 8 Add the opposite – 2. = 16 Add.
GUIDED PRACTICE 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. b. = (– 10) (– 4) Multiply 2 and – 5. = 40 Same signs; product is positive. c. 2 (– 5) (– 4) – 1 (– 4) (– 3) = 2 (– 3) 2 =– 6 1 Multiply – and – 4 2 Different signs; product is negative.
GUIDED PRACTICE Find the product. 1. – 2 (– 7) = (– 2) (– 7) = 14 2. – 0. 5 (– 4) (– 9) 3. 4 (– 3) (7) 3 Same signs; product is positive. = (2) (– 9) Multiply – 0. 5 and – 4. = – 18 Different signs; product is negative. Multiply 4 and – 3. 3 = – 4 (7) = – 28 Different signs; product is negative.
EXAMPLE 2 Identify properties of multiplication Statement Property illustrated a. (x · 7) · 0. 5 = x · (7 · 0. 5) b. 8 · 0 =0 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 Associative property of multiplication Multiplicative property of zero
GUIDED PRACTICE Identify the property illustrated. 1. – 1 · 8 = – 8 2. 12 · x = x · 12 3. (y · 4) · 9 = y · (4 · 9) 4. 0 · (– 41) = 0 5. – 5 · (– 6) = – 6 · (– 5) 6. 13 · (– 1) = – 13 Multiplicative property of – 1 Commutative property of multiplication Associative property of multiplication Multiplicative property of zero Commutative property of multiplication Multiplicative property of – 1
EXAMPLE 1 Find multiplicative inverses of numbers 1 a. The multiplicative inverse of – is – 5 because 5 – 1 · (– 5) = 1. 5 6 is 7 because – – b. The multiplicative inverse of 7 6 – 6 · – 7 = 1. 7 6
EXAMPLE 2 Divide real numbers Find the quotient. a. – 16 4 = – 4 b. – 20 – 5 = – 20 ·(-3/5) 3 = 12
GUIDED PRACTICE Find the multiplicative inverse of the number. 1. – 27 The multiplicative inverse of – 27 is – 1 because 27 1 = 1. – 27 2. – 8 The multiplicative inverse of – 8 is – 1 because 8 1 – = 1. – 8 8
GUIDED PRACTICE 3. – 4 7 The multiplicative inverse of – 4 is – 7 because 4 7 7 = 1. – 4· – 4 7 4. – 1 3 The multiplicative inverse of – 1 is – 3 because 3 – 1 · (– 3) = 1 3
GUIDED PRACTICE 5. – 64 ÷ (– 4) = 6. – 3 8 ÷ = 16 3 =– 3 10 8 =– 1 4 · 10 3
GUIDED PRACTICE 7. 18 ÷ – 2 18 · = 9 – 9 2 = – 81 2 8. – 2 ÷ 18 = – 5 5 =– 1 45 · 1 18
EXAMPLE 4 Simplify an expression 36 x – 24. 6 Simplify the expression 36 x – 24 = (36 x – 24) 6 = ( 36 x – 24) = 36 x · = 6 x – 4 ÷ 6 Rewrite fraction as division. · 1 6 Division rule 1 – 24 6 · 1 6 Distributive property Simplify.
GUIDED PRACTICE Simplify the expression 2 x – 8 1. – 4 2 x – 8 – 4 = ( 2 x – 8 ) ÷ 4 1 = ( 2 x – 8 ) · – 4 1 – 8 – 1 = 2 x · – · 4 4 1 = – x+2 2 Rewrite fraction as division. Division rule Distributive property Simplify.
GUIDED PRACTICE 2. – 6 y +18 3 – 6 y + 18 (– 6 y + 18) ÷ 3 = (– 6 y + 18) · 1 3 1 = – 6 y · 1 + 18 · 3 3 = – 2 y + 6 Rewrite fraction as division. Division rule Distributive property Simplify.
GUIDED PRACTICE 3. – 10 z – 20 – 5 – 10 z – 20 Rewrite fraction as division. = (– 10 z – 20) ÷ – 5 Division rule = (– 10 z – 20) · – 1 5 = – 10 z · – 1 · – 20 · – 1 Distributive property 5 5 = 2 z + 4 Simplify.
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