Identity and Inverse
Identity and Inverse of Addition
Additive Inverse: the sum of a number and its opposite is 0
a + (­a) = 0
­a + a = 0
Identity and Inverse
Additive Identity: the number you can add by and still get
the same number
Additive Identity Property of Zero:
a+0=a
Engage New York: Module 3, Lesson 5
Write the sum. Then write an equivalent expression by combining
like­terms and removing parentheses.
A. 2x and ­2x + 3
B. 2x ­ 7 and the opposite of 2x
C. The opposite of (5x ­ 1) and 5x
Write the sum. Then write an equivalent expression by combining
like­terms and removing parentheses.
D. ­4 and 4b + 4
E. 3x and 1 ­ 3x
F. The opposite of 4x and ­5 + 4x
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Identity and Inverse
Identity and Inverse of Multiplication
Multiplicative Inverse: the product of a number and its
multiplicative inverse is 1. The multiplicative inverse is the
reciprocal of a number.
a 1
a=1
Write the product and then write the expression in standard form
by removing parentheses and combining like­terms.
1 and (2x ­ 1)
A. The multiplicative inverse of 5
5
Multiplicative Identity: the number you can multiply by and
still get the same number
Multiplicative Identity Property of One:
a 1=a
B. The multiplicative inverse of 2 and (2x + 4)
C. The multiplicative inverse of 4 and 4h ­ 20
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