 # Using the Identity and Inverse to Write Equivalent Expressions

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Examples, videos, and solutions to help Grade 7 students learn how to use identity and inverse to write equivalent expressions.

### New York State Common Core Math Grade 7, Module 3, Lesson 5

Download worksheets for Grade 7, Module 3, Lesson 5

### Lesson 5 Student Outcomes

• Students recognize the identity properties of 0 and 1 and the existence of inverses (opposites and reciprocals) to write equivalent expressions.

### Lesson 5 Closing

• Additive inverse and multiplicative inverse; the sum of additive inverses equals 0; the product of multiplicative inverses equals 1.
• The Additive Identity Property of Zero states that zero is the only number that when summed to another number, the result is again that number. The Multiplicative Identity Property of One states that one is the only number that when multiplied with another number, results in that number again.

Classwork

Opening Exercise
1. In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. Write an expression representing the temperature change. What was the afternoon temperature?

2. Rewrite subtraction as adding the inverse for the following problems, and find the sum. a. 2 - 2
b. -4 - (-4)
c. The difference of 5 and 5.
d. g - g

3. What pattern can you deduce from Opening Exercises 1 and 2?

4. Add or subtract.
a. 16 + 0
b. 0 - 7
c. -4 + 0
d. 0 + d
e. What pattern do you notice in (a)–(d)?

5. Your younger sibling runs up to you and excitedly exclaims, "I'm thinking of a number. If I add it to the number 2 ten times, that is, 2 + my number my number my number... and so on, then the answer is 2. What is my number?" You almost immediately answer, "zero," but are you sure? Can you find a different number (other than zero) that has the same property? If not, can you justify that your answer is the only correct answer?

Example 1
Write the sum and then write an equivalent expression by collecting like terms and removing parentheses.

Exercise 1
Write the sum and then write an equivalent expression by collecting like terms and removing parentheses whenever possible.

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)
b. b. The multiplicative inverse of 2 and (2x + 4)

Exercise 2
Write the product and then write the expression in standard form by removing parentheses and combining like terms. Justify each step.

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