This document discusses adding integers. It defines additive inverses as two numbers with a sum of zero, such as 23 and -23. When adding opposites, their sum is zero. To add integers that are not opposites, number lines can be used. An example word problem involves subtracting 8 yards and adding 3 yards for a football team, resulting in a loss of 5 yards. The rules for adding integers are provided: numbers with the same sign are added, numbers with different signs are solved by subtracting the digits and keeping the sign of the larger number.

1. ADDING
INTEGERS
1-5

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

3. ADDITION OF OPPOSITES
 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

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

5. WORD PROBLEM…
 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

6. 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?
 Steps:
1. Start at 0
2. To represent -8, move to the left 8 places.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

7. 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.
4. Since we end on -5, our result to the problem is -5.
So, -8 +3 = -5 …
The result of the first two plays is a loss of 5 yards.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

8. ADDITION RULES
1. 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
2. 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

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

10. Examples…
1.) -1 + 4
2.) 7 + (-3)
3.) -2 + (-2)
4.) 6 + (-9)
= 3
= 4
= -4
= -3