Adding Integers
There are two cases when adding Integers or signed numbers.
Case I - Integers with the same sign.
Ex 1: -3 + -4
-3 + -4 = -7
Case II - Integers with the different sign.
Ex 2: -5 + 7 Ex 3: 4 + -9
-5 + 7 = 2 4 + -9 = -5
You try it!
1) -7 + 32)3)
4) 19.31 - -4.58 5) -58 + -276) 62 + -35
7) Use the number lines, to find the sum of each problem.
-4 + 9 = ___
-3 + -8 = ___
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
Case II: Integers with the Different signs.
Ex 2: -3 - -5
Step 1: -3 + 5
Step 2: -3 + 5 = 2
You try it!
1) -4 - 32) 3) 8 - -5
4) -9.36 – 5.25) -50 - 386) -35 - 35
7) Use the number lines, to find the difference of each problem.
4 - 12 = ___
-6 - (-3) = ___
-2 - 4 = ___
Word Problems
8) If the overnight temperature at the Arctic Circle was -14F, and the temperature rose 8F 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 136F, while the lowest was -129F 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 ÷-4Ex 2: 2 x 5
-32 ÷-4 = 8 2 x 5 = 10
Case II - Integers with DIFFERENT signs.
Ex 1: -48 ÷6Ex 2: 7 x -9
-48 ÷6 = -8 7 x -9 = -63
You try it!
1) (-2)3 x (-3)2 2) -81 ÷ -93) -5 4
4) -12 -6 5) –2.4 .006 6) -125 ÷ 5
7) 64 ÷ -4 ÷ -4 8) -5 -2 -3 9) (-5)3 2
(-1)n What happens if n is a odd #? An even #?
Absolute Value
You try it!
1) = _____ 2) = ____
3) _____ 4) = ___
5) = _____ 6)=____
Order of Operations
You try it!
1) 5 + 16 ÷ 23 2) 4(7 + 3) – 9 3) 2(20 – -8) ÷ 7
4) 5) (-4 + -6) ÷ 6) -28 + 63 ÷ - 7
7) ÷ 3 + 14 · 12 8) 32 (8 + -6) - -2 9) 96 + · -2
Comparing and Ordering Integers
You try it!
- State the opposite of each.
a) -2 ___ b) +5 ___ c) -13 ___ d) 0 ___
2. Compare using >, <, =.
a) -3 ___-4 b) -6 ___ +5 c) -13 ___ 0
d) 99 ___ -100 e) ___ f) ___
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, 1.5, -3, 2