ADDING INTEGERS 1 5 VOCABULARY 1 Additive Inverses

ADDING INTEGERS 1 -5

VOCABULARY… 1. Additive Inverses – two numbers with a sum of zero ex. ) 23 and -23 are additive inverses, because 23 + (-23) = 0

ADDITION OF OPPOSITES n n When you add two opposites, their sum is zero. So, opposites are called additive inverses when you’re adding them together. Therefore, the sum of an integer and its opposite is always zero (0). 1 + (-1) = 0 -1 + 1 = 0

NUMBER LINES… n Number lines are an excellent way to add positive and negative numbers that are not opposites. -3 -2 -1 0 1 2 3

WORD PROBLEM… n On the first play of their drive, a football team loses 8 yards. The next play, they gain 3 yards. What is their yardage for the team’s first two plays? First Play + Second Play -8 3

On the first play of their drive, a football team loses 8 yards. The next play, they gain 3 yards. What is their yardage for the team’s first two plays? n Steps: 1. Start at 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 2. To represent -8, move to the left 8 places. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 1

On the first play of their drive, a football team loses 8 yards. The next play, they gain 3 yards. What is their yardage for the team’s first two plays? 3. To add positive 3, move to the right 3 places. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 4. 1 Since we end on -5, our result to the problem is -5. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 So, -8 +3 = -5 … The result of the first two plays is a loss of 5 yards.

ADDITION RULES 1. 2. To add two numbers with the same sign, add the numbers together. The answer will have the same sign as the numbers. ex. ) 3 + 5 = 8 -3 + (-5) = -8 To add two numbers with different signs, take the bigger digit and subtract the other digit. Your answer will have the same sign as the bigger digit. ex. ) -3 + 5 = 2 3 + (-5) = -2

SIGNS FOR ADDITION (+ ) + ( + ) = + (-) + ( -) = (+ ) + ( -) = (-) + ( + ) = Subtract the digits and keep the sign of the larger digit.