<ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your assignment out on your desk. </li></ul></ul><ul><ul><li>H...
<ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your assignment out on your desk. </li></ul></ul><ul><ul><li>H...
Addition of Integers Section 2.2 P. 63
Properties of Addition <ul><li>Commutative Property : - the  order   in which two numbers are added does NOT change the su...
Properties of Addition <ul><li>Additive Identity Property : </li></ul><ul><ul><li>The  sum   of a number and the additive ...
Properties of Addition <ul><li>Additive Inverse Property : </li></ul><ul><li>The sum of a number and its  opposite   is 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) = -...
<ul><li>Think what these two problems have in common.  </li></ul><ul><li>1. You had to add the 3 and the 5 to get the answ...
<ul><li>Rule:  </li></ul><ul><li>To add numbers with the same sign,  </li></ul><ul><ul><li>ADD the numbers. </li></ul></ul...
EXAMPLE 1 Adding Integers Using a Number Line Use a number line to find the sum. a. 5 + (  8) – Start at  0 . Move  5  uni...
EXAMPLE 1 Adding Integers Using a Number Line Use a number line to find the sum. a. 5 + (  8) – Start at  0 . Move  5  uni...
EXAMPLE 1 Adding Integers Using a Number Line Use a number line to find the sum. b.   – 6 + 10 Start at  0 . Move  6  unit...
EXAMPLE 1 Adding Integers Using a Number Line Use a number line to find the sum. b.   – 6 + 10 Start at  0 . Move  6  unit...
<ul><li>Rule: </li></ul><ul><li>To add numbers with opposite signs  </li></ul><ul><ul><li>Subtract the numbers. </li></ul>...
<ul><li>5 + (-3) =  </li></ul><ul><li>The signs are opposite so subtract.  </li></ul><ul><li>5 has the larger absolute val...
<ul><li>Apply the rules: </li></ul><ul><li>-8  +  -12  = ___  5 +  -9  = _____ </li></ul><ul><li>-6  +  15  = _____  - 4 +...
<ul><li>Apply the rules: </li></ul><ul><li>-8  +  -12  = ___  5 +  -9  = _____ </li></ul><ul><li>-6  +  15  = _____  - 4 +...
<ul><li>Assignment:  </li></ul><ul><li>P 65 #1-23 </li></ul><ul><li>In 12-23 there are  three  problems that need to have ...
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2.2 add integers ws day1

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2.2 add integers ws day1

  1. 1. <ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your assignment out on your desk. </li></ul></ul><ul><ul><li>Have your covered textbook with you. </li></ul></ul><ul><ul><li>94 x 8= </li></ul></ul><ul><ul><li>55.07 – 9.26= </li></ul></ul>
  2. 2. <ul><li>Before the bell rings... </li></ul><ul><ul><li>Have your assignment out on your desk. </li></ul></ul><ul><ul><li>Have your covered textbook with you. </li></ul></ul><ul><ul><li>94 x 8= </li></ul></ul><ul><ul><li>55.07 – 9.26= </li></ul></ul>752 45.81
  3. 3. Addition of Integers Section 2.2 P. 63
  4. 4. Properties of Addition <ul><li>Commutative Property : - the order in which two numbers are added does NOT change the sum. 4 + -8 = - 8 + 4 </li></ul><ul><li>Associative Property : The way you group three numbers when adding does NOT change the sum. </li></ul><ul><li>(-5 + 8) + 9 = -5 + ( 8 + 9 ) </li></ul>
  5. 5. Properties of Addition <ul><li>Additive Identity Property : </li></ul><ul><ul><li>The sum of a number and the additive identity – ZERO- is always the number. </li></ul></ul><ul><ul><li>Example: 4 + 0 = 4 </li></ul></ul><ul><ul><li> -19 + 0 = -19 </li></ul></ul><ul><ul><li>a + 0 = a </li></ul></ul>
  6. 6. Properties of Addition <ul><li>Additive Inverse Property : </li></ul><ul><li>The sum of a number and its opposite is 0. a + (- a ) = 0 -4 + 4 = 0 </li></ul><ul><li>8 + -8 = 0 </li></ul>
  7. 7. 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 more If you owe $5 and then borrow $3 more, how much do you have?
  8. 8. <ul><li>Think what these two problems have in common. </li></ul><ul><li>1. You had to add the 3 and the 5 to get the answer. </li></ul><ul><li>2. The sign depended on the sign of the original numbers. </li></ul>
  9. 9. <ul><li>Rule: </li></ul><ul><li>To add numbers with the same sign, </li></ul><ul><ul><li>ADD the numbers. </li></ul></ul><ul><ul><li>KEEP THE SIGN of the numbers involved. </li></ul></ul>
  10. 10. 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.
  11. 11. 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 .
  12. 12. 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.
  13. 13. 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 .
  14. 14. <ul><li>Rule: </li></ul><ul><li>To add numbers with opposite signs </li></ul><ul><ul><li>Subtract the numbers. </li></ul></ul><ul><ul><li>Keep the sign of the number with the larger absolute value. </li></ul></ul>
  15. 15. <ul><li>5 + (-3) = </li></ul><ul><li>The signs are opposite so subtract. </li></ul><ul><li>5 has the larger absolute value so the answer is positive. </li></ul><ul><li>-5 + 3 = </li></ul><ul><li>The signs are opposite so subtract. </li></ul><ul><li>5 has the larger absolute value so the answer is negative. </li></ul>
  16. 16. <ul><li>Apply the rules: </li></ul><ul><li>-8 + -12 = ___ 5 + -9 = _____ </li></ul><ul><li>-6 + 15 = _____ - 4 + -3 + -7 = _____ </li></ul><ul><li>7 + 5 = _____ -5 + 3 + 5 + -8 = ___ </li></ul><ul><li>-7 + 7 = ____ -13 + 0 =____ </li></ul>
  17. 17. <ul><li>Apply the rules: </li></ul><ul><li>-8 + -12 = ___ 5 + -9 = _____ </li></ul><ul><li>-6 + 15 = _____ - 4 + -3 + -7 = _____ </li></ul><ul><li>7 + 5 = _____ -5 + 3 + 5 + -8 = ___ </li></ul><ul><li>-7 + 7 = ____ -13 + 0 =____ </li></ul>-20 -4 9 -14 12 -13 0 -5
  18. 18. <ul><li>Assignment: </li></ul><ul><li>P 65 #1-23 </li></ul><ul><li>In 12-23 there are three problems that need to have either the Identity Property (adding 0) or the Inverse Property (adding opposites) listed with them. </li></ul><ul><li>Show work and NO CALCULATORS </li></ul>

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