Engage NY MODULE 3 LESSON 5: USING THE IDENTITY AND INVERSE TO WRITE EQUIVALENT EXPRESSIONS
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1 Engage NY MODULE 3 LESSON 5: USING THE IDENTITY AND INVERSE TO WRITE EQUIVALENT EXPRESSIONS "Grade 7 Mathematics Module 3." Grade 7 Mathematics Module 3. 9 Sept Web. 26 Jan <
2 Opening Exercise In the morning, Harrison checked the temperature outside to find that it was -12 o F. Later in the afternoon, the temperature rose to 12 o F. Write an expression representing the temperature change. What was the afternoon temperature? The afternoon temperature was 0 o F.
3 Opening Exercise Rewrite subtraction as adding the inverse (copy, add, opposite) for the following problems and find the sum. a (-2) 2 + (-2) = 0
4 Opening Exercise Rewrite subtraction as adding the inverse (copy, add, opposite) for the following problems and find the sum. b. -4 (-4) = 0
5 Opening Exercise Rewrite subtraction as adding the inverse (copy, add, opposite) for the following problems and find the sum. c. The difference of 5 and (-5) 5 + (-5) = 0
6 Opening Exercise Rewrite subtraction as adding the inverse (copy, add, opposite) for the following problems and find the sum. d. g g g + (-g) g + (-g) = 0
7 Opening Exercise What pattern do you notice in Opening Exercises 1 and 2? The sum of a number and its additive inverse is equal to zero.
8 Opening Exercise Add or subtract. a
9 Opening Exercise Add or subtract. b (-7) = -7
10 Opening Exercise Add or subtract. c
11 Opening Exercise Add or subtract. d. 0 + d d
12 Opening Exercise e. What pattern do you notice in parts (a) through (d)? The sum of any quantity and zero is equal to the value of the quantity.
13 Example 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses. a. 2x and -2x + 3 2x + (-2x + 3) (2x + (-2x)) + 3 Associative property, collect like terms Additive inverse 3 Additive identity property of zero
14 Example 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses. b. 2x 7 and the opposite of 2x 2x 7 + (-2x) 2x + (-2x) + (-7) Commutative property, associative property 0 + (-7) Additive inverse -7 Additive identity property of zero
15 Example 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses. c. The opposite of (5x 1) and 5x -(5x 1) + 5x -1(5x 1) + 5x Taking the opposite is equivalent to multiplying by -1-5x x Distributive property (-5x + 5x) + 1 Commutative property, any order property Additive inverse 1 Additive identity property of zero
16 Exercise 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses wherever possible. a. -4 and 4b (4b + 4) (-4 + 4) + 4b Any order, any grouping 0 + 4b Additive inverse 4b Additive identity property of zero
17 Exercise 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses wherever possible. b. 3x and 1 3x 3x + (1 3x) 3x + (1 + (-3x)) Subtraction as adding the inverse (3x + (-3x)) + 1 Any order, any grouping Additive inverse 1 Additive identity property of zero
18 Exercise 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses wherever possible. c. The opposite of 4x and x -4x + (5 + 4x) (-4x + 4x) + (-5) Any order, any grouping 0 + (-5) Additive inverse -5 Additive identity property of zero
19 Exercise 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses wherever possible. d. The opposite of -10t and t 10t 10t + (t 10t) (10t + (-10t)) + t Any order, any grouping 0 + t Additive inverse t Additive identity property of zero
20 Exercise 1 Write the sum and then write an equivalent expression by collecting like terms and removing parentheses wherever possible. e. The opposite of (-7 4v) and -4v -(-7 4v) + (-4v) -1(-7 4v) + (-4v) Taking the opposite is equivalent to multiplying by v + (-4v) Distributive property Any grouping, Additive inverse 7 Additive identity property of zero
21 Example 2 ( 3 ) 4 (4) = = = 1 9 (- 1 ) (-3) = 1 3 What are these pairs of numbers called? Reciprocal What is another term for reciprocal? Multiplicative inverse (- 6 5 ) (- 5 6 ) = 1
22 Example 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. a. The multiplicative inverse of 1 5 and 2x 1 5 5(2x 1 5 ) 5(2x) 5( 1 5 ) 10x 1 Distributive property Multiplicative inverses
23 Example 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. b. The multiplicative inverse of 2 and 2x (2x + 4) (2x) + 1 (4) Distributive property 2 2 1x + 2 Multiplicative inverses, multiplication x + 2 Multiplicative identity property of one
24 Example 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. c. The multiplicative inverse of ( 1 3x+5 ) and 1 3 (3x + 5) 1 3 3x( 1 )+ 3 5(1 ) Distributive property 3 1x + 5 Multiplicative inverse 3 x + 5 Multiplicative identity property of one 3
25 Exercise 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. a. The reciprocal of 3 and -6y 3x ( 1 )(-6y + (-3x)) Rewrite subtraction as an addition problem 3 ( 1 )(-6y) + 3 (1 )(-3x) Distributive property 3-2y 1x Multiplicative inverse -2y x Multiplicative identity property of one
26 Exercise 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. b. The multiplicative inverse of 4 and 4h 20 ( 1 )(4h+ (-20)) Rewrite subtraction as an addition problem 4 ( 1 )(4h) + 4 (1 )(-20) Distributive property 4 1h + (-5) Multiplicative inverse h 5 Multiplicative identity property of one
27 Exercise 2 Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step. c. The multiplicative inverse of and j (-6)(2 + (- 1 j)) Rewrite subtraction as an addition problem 6 (-6)(2) + (-6)(- 1 j) Distributive property j Multiplicative inverse j Multiplicative identity property of one
28 Homework Problem Set #1-4 Study for Engage NY Lessons 4-6 quiz Friday
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Page 1 Month Unit Content Section Benchmarks Description Sept 4- Oct Unit 1: 3 Whole # and decimal operations 1.1, 1.2, 1.5, 1.7, 1.8, 1.9,2.1, 2.3, 2.4, 2.6, 2.8 6.2.2.1 Apply the associative, commutative
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In the previous set of notes we looked at vertical shifts, where the graph of some iginal function was moved up down by adding numbers to subtracting numbers from the outputs of a function. In this set