Before the bell rings... Have your assignment out on your desk. Have your covered textbook with you.

4. 94 x 8=

6. 55.07 – 9.26=

Before the bell rings... Have your assignment out on your desk. Have your covered textbook with you.

4. 94 x 8=

6. 55.07 – 9.26=

752

45.81

Addition of IntegersAddition of Integers

Section 2.2Section 2.2

P. 63P. 63

Properties of AdditionProperties of Addition

Commutative PropertyCommutative Property: - the : - the orderorder in in which two numbers are added does NOT which two numbers are added does NOT change the sum. 4 + -8 = - 8 + 4change the sum. 4 + -8 = - 8 + 4

Associative PropertyAssociative Property: The way you : The way you groupgroup three numbers when adding does NOT three numbers when adding does NOT change the sum. change the sum.

(-5 + 8) + 9 = -5 + ( 8 + 9 )(-5 + 8) + 9 = -5 + ( 8 + 9 )

Properties of AdditionProperties of Addition

Additive Identity PropertyAdditive Identity Property:: The The sumsum of a number and the additive identity of a number and the additive identity

– – ZERO-ZERO- is always the number.is always the number.

Example: 4 + 0 = 4Example: 4 + 0 = 4

-19 + 0 = -19-19 + 0 = -19

a + 0 = aa + 0 = a

Properties of AdditionProperties of Addition

Additive Inverse PropertyAdditive Inverse Property:: The sum of a number and its The sum of a number and its oppositeopposite is 0.is 0.

a + (- a ) = 0a + (- a ) = 0 -4 + 4 = 0 -4 + 4 = 0

8 + -8 = 0 8 + -8 = 0

5 + 3 = 8 Up 5 , then up 3 more If you have $5 in your pocket and are given $3 more, how much do you have?

-5 + (-3) = -8 Down 5 then down 3 moreIf you owe $5 and then borrow $3 more, how much do you have?

Think what these two problems have in Think what these two problems have in common. common.

1. You had to add the 3 and the 5 to get 1. You had to add the 3 and the 5 to get the answer. the answer.

2. The sign depended on the sign of the 2. The sign depended on the sign of the original numbers.original numbers.

Rule: Rule: To add numbers with the same sign, To add numbers with the same sign,

ADD the numbers.ADD the numbers.

KEEP THE SIGN of the numbers involved.KEEP THE SIGN of the numbers involved.

EXAMPLE 1 Adding Integers Using a Number Line

Use a number line to find the sum.

a. 5 + ( 8)–

Start at 0. Move 5 units to the right. Then move 8 units to the left.

EXAMPLE 1 Adding Integers Using a Number Line

Use a number line to find the sum.

a. 5 + ( 8)–

Start at 0. Move 5 units to the right. Then move 8 units to the left.

Answer

The final position is –3. So, 5 + (–8) = –3.

EXAMPLE 1 Adding Integers Using a Number Line

Use a number line to find the sum.

b. –6 + 10

Start at 0. Move 6 units to the right. Then move 10 units to the left.

EXAMPLE 1 Adding Integers Using a Number Line

Use a number line to find the sum.

b. –6 + 10

Start at 0. Move 6 units to the right. Then move 10 units to the left.

Answer

The final position is 4. So, –6 + 10 = 4.

Rule:Rule: To add numbers with opposite signs To add numbers with opposite signs

Subtract the numbers.Subtract the numbers.

Keep the sign of the number with the Keep the sign of the number with the larger absolute value.larger absolute value.

5 + (-3) = 5 + (-3) = The signs are opposite so subtract. The signs are opposite so subtract.

5 has the larger absolute value so the answer is 5 has the larger absolute value so the answer is positive.positive.

-5 + 3 = -5 + 3 = The signs are opposite so subtract. The signs are opposite so subtract.

5 has the larger absolute value so the answer is 5 has the larger absolute value so the answer is negative.negative.

Apply the rules:Apply the rules:

-8 + -12 = ___ 5 + -9 = _____-8 + -12 = ___ 5 + -9 = _____

-6 + 15 = _____ - 4 + -3 + -7 = _____-6 + 15 = _____ - 4 + -3 + -7 = _____

7 + 5 = _____ -5 + 3 + 5 + -8 = ___7 + 5 = _____ -5 + 3 + 5 + -8 = ___

-7 + 7 = ____-7 + 7 = ____ -13 + 0 =____-13 + 0 =____

Apply the rules:Apply the rules:

-8 + -12 = ___ 5 + -9 = _____-8 + -12 = ___ 5 + -9 = _____

-6 + 15 = _____ - 4 + -3 + -7 = _____-6 + 15 = _____ - 4 + -3 + -7 = _____

7 + 5 = _____ -5 + 3 + 5 + -8 = ___7 + 5 = _____ -5 + 3 + 5 + -8 = ___

-7 + 7 = ____-7 + 7 = ____ -13 + 0 =____-13 + 0 =____

-20 -4

9 -14

12

-130

-5

Assignment: Assignment:

P 65 #1-23P 65 #1-23

In 12-23 there are In 12-23 there are threethree problems problems that need to have either the that need to have either the Identity Identity PropertyProperty (adding 0) or the (adding 0) or the Inverse Inverse PropertyProperty (adding opposites) listed with (adding opposites) listed with them.them.

Show work and Show work and NO CALCULATORSNO CALCULATORS