Chapter 2 Intervention Lesson 2

​Generating Equivalent Expressions

Chapter 2 Intervention Lesson 1

​Additive Inverse

​The Inverse Property of Addition

• Additive Inverses have a sum of zero

• Example:

  • The Additive Inverse of 1 is -1

  • Because 1 + (-1) = 0​

Inverse = Opposite​

• ​Copy this table into your notebook.

• Fill in the center column with the additive inverse.

• ​Show proof that they are opposite.

​

​Don't forget to add this to your table of contents!

​Find the Additive Inverse

​

stick = x

string = 4x​

​stick + string = total length

x + 4x = 15

5x = 15

x = 3​

4x = 12

The String is 12 meters long. ​

​Solving Example:

A stick is 𝑥 meters long. A string is 4 times as long as the stick.

• ​Express the length of the string in terms of 𝑥.

• If the total length of the string and the stick is 15 meters long, how long is the string?​

​Word Problem:

​Expressions from Word Problems

Now it's your turn... ​

​Multiplicative Inverse

​The Inverse Property of Multiplication

Inverse = Opposite​

• Find the Multiplicative Inverse​

• ​Write out the proof showing the product is 1.

• ​Use the multiplicative inverse to write each expression in standard form (evaluate the expression)

​

​Read through the example!!!

​Multiplicative Inverse: Copy this table into your math notebook!

​

​Take these Notes...

​Example Problem #1: Two Ways to Solve

4y​ - (3 + y) ; if y = 2

4 (2) - (3 + 2)

4 (2) - (5)

8 - 5

3​

​

Option 1: Order of Operations Option 2: Properties of Addition

4y​ - (3 + y) ; if y = 2

4y - 3 - y

3y - 3​

3 (2) - 3​

6 - 3

3​

​

​Take these Notes...

​Example Problem #2: Two Ways To Solve

Option 1: Order of Operations Option 2: Properties of Addition

(7 + w) - (w + 7)​ ; if w = -4

(7 + (-4)) - (-4 + 7)

(7 - 4) - (-4 + 7)

3 - (3)​

3 - 3

​0

​

(7 + w) - (w + 7)​ ; if w = -4

7 + w - w - 7

w - w + 7 - 7​

0 w​ + 0

0​

​

​

​Example Problem #1:

​Take Notes... 2 Ways to Solve!

When multiplying by a fraction, can divide by the inverse! ​

​Example Problem #1:

​Multiplicative Inverse

​Now your turn to try!