Adding Integers
There are two cases when adding Integers or signed numbers.
Case I
- Integers with the same sign.
Ex 1: -3 + -4
 Add Integers
 Keep the Sign
3 + -4 = -7
-
Case II -
Integers with the different sign.
Ex 2: -5 + 7
7
- 5
2
Ex 3: 4 + -9
 Subtract Integers
 Keep the Sign of the number with
the highest absolute value
9
- 4
5
5+7=2
4 + -9 = -5
-
You try it!
-
1)
7+3
4) 19.31 - -4.58
2)
3
1
7
 4
2
8
5) -58 + -27
3)
6) 62 + -35
7) Use the number lines, to find the sum of each problem.
-
4 + 9 = ___
-
3 + -8 = ___
1
5
 8  ( 4 )
3
9
Word Problems
8) You park in a garage 3 floors below ground level. Then
you get in the elevator and go up 12 floors. Write an
addition sentence to represent this situation.
9) A research team aboard an underwater research
vessel descends 1,500 feet beneath the surface of the
water. They then rise 525 feet and descend again 350
feet. Write an addition sentence to represent this
situation.
10) Peter weighs 156 pounds, but he would like to wrestle
in a lower weight class. He loses 4 pounds one week, gains
back 2 pounds the next week, loses 5 pounds the third
week, and loses 3 pounds the fourth week. Write an
addition sentence to represent this situation.
SUBTRACTING INTEGERS
Case I: Integers with the same signs.
Ex 1: -4 - 6
Step 1: Since the integers have the same sign, you can just add them!
Step 2: -4 + -6
Step 3: -4 - 6 = -10
(same signs
add)
Case II: Integers with the Different signs.
 Change double negative to a positive
 Use addition rules
Ex 2: -3 - -5
Step 1: -3 + 5
Step 2: -3 + 5 = 2
(different signs
subtract)
You try it!
1)
-
4 - 3
4) -9.36 – 5.2
2)

3
5
4  2 
5
8
5) -50 - 38
3) 8 - -5
6)
7) Use the number lines, to find the difference of each problem.
4 - 12 = ___
-
6 - (-3) = ___
-
2 - 4 = ___
-
35 - 35
Word Problems
8) If the overnight temperature at the Arctic Circle was -14F, and
the temperature rose 8F during the day, how many degrees warmer
was it during the day than during the overnight?
9) The highest recorded temperature on Earth was recorded in
Africa at 136F, while the lowest was -129F in Antarctica. What is
the difference between these extreme temperatures?
10) Use the thermometers to determine how much warmer the
temperature was at 12:00 P.M. than 8:00 A.M.
Multiplying and Dividing Integers
There are two cases when multiplying and dividing Integers or signed numbers.
Case I
- Integers with the SAME signs.
Ex 1:
32 ÷ -4
-
-
-
2 x 5 = 10
 Multiply or Divide
 Answer is Negative
Ex 2:
48 ÷ 6 = -8
You try it!
3
1) (-2) x (-3)2
4) -12 
-
7 x -9
7 x -9 = -63
2) -81 ÷
-
9
5) –2.4  .006
6
7) 64 ÷ -4 ÷ -4
(-1)n
2 x 5
- Integers with DIFFERENT signs.
48 ÷ 6
-
Ex 2:
32 ÷ -4 = 8
Case II
Ex 1:
 Multiply or Divide
 Answer is Positive
8) -5  -2  -3
3)
6)
-
-
5  4
125 ÷ 5
9) (-5)3  2
What happens if n is a odd #? An even #?
 The distance a number is from zero
 Always a positive answer!!
Absolute Value
You try it!
1)
5 = _____
2)  100 = ____
3)
7  15 _____
4) 23  10 = ___
5)
2  5 = _____
6) 36  24 =____
Order of Operations
P- Parenthesis ( )
E- Exponents (also
includes square roots)
M- Multiplication
D- Division
A- Addition
S- Subtraction
 the order in which you should perform the different
types of operations in a problem
 Remember: PEMDAS
You try it!
1)
4)
7)
5 + 16 ÷ 23
24   3
3
225 ÷ 3 + 14 · 12
2)
4(7 + 3) – 9
3)
5)
(-4 + -6) ÷  5
6)
8)
32 (8 + -6) - -2
9)
2(20 – -8) ÷ 7
-
28 + 63 ÷ - 7
96 +
82
· -2
5
Comparing and Ordering Integers
 Use the number line to help you.
 Numbers to the right are always greater!
 Opposites are numbers that are the same distance
from 0 but on different sides of 0.
You try it!
1. State the opposite of each.
a) -2 ___
b) +5 ___
c) -13 ___
d) 0 ___
2. Compare using >, <, =.
a) -3 ___-4
b) -6 ___ +5
d) 99 ___ -100
e)
5
___
6
c) -13 ___ 0
f)
4
___
3. Order the integers in each set from least to greatest.
{ -54, 22, 6, -69, -90, 0 }
4. Place the following #’s on the # line below.
-4, 3, -4 3 , 1.5, -3, 2
4
4