Name __________________________________

Period __________

Date:

Topic: 1-4 Sums and Differences

Essential Question: Why is subtracting a negative number

like adding a positive number?

Standard: 9-12.A.1.18 Use the four basic operations (+, -, ×, ÷) with linear, polynomial, and rational expressions in contextual situations.

Objective:

Identity Property:

Property of

Opposites:

(

)

( )

To review the rules for adding and subtracting real numbers.

In arithmetic you learned to add positive numbers (4 + 7 = 11)

and to subtracta smaller positive number from a larger one

(12 7 = 5). In this lesson youwill review how to add and

subtract any real numbers, positive or not.

The identity property of addition tells you how to add zero and

any givennumber:

The sum is the given number.

The property of opposites tells you that the

sum of opposites is zero.

Summary

2

Rules for Addition:

1. If a and b are negative numbers, thena + b is negative

and

(| | | |)

( ) (| | | |)

( )

2. If a is a positive number, b is a negativenumber, and

|a| is greater than |b|, then a + b is a positive number

and

| | | |

( ) (| | | |)

3. If a is a positive number, b is a negativenumber, and

|a| is less than |b|, thena + b is a negative number and

(| | | |)

( ) (| | | |)

( )

3

Summary:

Commutative:

The sign of a positive number is plus and the sign of a negative

number is minus. A positive and a negative number have

opposite signs.

The above rules can be summarized as follows:

If two numbers have the same sign, add their absolute

values and keep the common sign.

( ) (| | | |)

( )

If two numbers have opposite signs, subtract the

smaller absolute value from the larger absolute value

and keep the sign of the number with the larger

absolute value.

( ) (| | | |)

( )

Since addition of real numbers is commutative, these rules also

cover sums like,

and

4

Example 1:

Solution 1

Solution 2

Exercise 1:

Simplify ( ) ( )

Add the terms in order from left to right.

( ) ( )

( ) ( )

( )

( )

Use the commutative and associative properties to order and

group the termsconveniently.

( ) ( )

[ ( ) ( )] [ ]

Simplify ( ) ( )

5

Definition of

Subtraction:

Example 2:

Exercise 2:

For all real numbers a and b,

( )

Symbolically,

( )

To subtract any real number, add its opposite.

( )

( )

( )

( )

Simplify the following: Do not use a calculator.

( )

6-13.4

6

Example 3:

Solution 1

Solution 2

Exercise 3:

Simplify .

Add the terms in order from left to right.

Use the commutative and associative properties to order and group

the termsconveniently.

[ ] [( ) ( )]

( )

Simplify . Do not use a calculator.

7

Distributive

Property:

Example 4:

Exercise 4:

( )

( )

( )

( )

You know that multiplication is distributive with respect to

addition. Since subtraction is just the addition of an opposite,

multiplication is also distributive with respect to subtraction.

Simplify ( )

Remember that and are similar terms and can be

combined. Similar terms are also called like terms.

Simplify ( ) ( )

Temperatures on the planet Mars range from 122.2 C to

30.5 C. Find the difference between these two temperatures.

Class work: Page 23: Oral Exercises: 1-29

Homework: Page 24: 2-48 even, 51-53