Download SEEING HOW INTEGERS WORK Adding positive integers is like the

SEEING HOW INTEGERS WORK
Adding positive integers is like the temp.going up on a thermometer – a rise.
Adding negative integers is like the temp. going down on a thermometer – a drop.
Examples: Start at zero on the thermometer ~
a) (+5) + (+3) = go up 5 degrees, and then go up 3 more. Result equals +8.
b) (+7) + (-10) = go up 7 degrees, and then go down 10 degrees. Result equals -3.
Integer Addition:
 If the signs are the same, you find the sum of the numbers and use their sign.
Examples:
(+ 3) + (+ 2) Find the sum (add) and then use the positive sign. Answer = + 5
(- 5) + (- 5) Find the sum (add) and then use the negative sign. Ans. Is neg - 10
 If the signs are different, you find the difference of the numbers and use the
sign of the larger number (not including the numbers’ sign, + or -).
(- 10) + ( + 4) Find the difference (subtract: 10 - 4 = 6) and use the sign of the
larger number (-10), which is negative. So the answer becomes negative 6, (-6).
Integer Subtraction: When working with subtraction, it’s wise to rewrite the
question as an Addition question before continuing with the calculations:
 Subtracting a positive integer, takes away its positive direction, so it becomes
the same as adding a negative integer: - (+ 4) becomes + (- 4).
 Subtracting a negative integer, takes away its negative direction, so it becomes
the same as adding a positive integer: - (- 4) becomes + (+ 4)
Examples: Start at the place of the first number on the thermometer ~
a)
(- 3) – (+ 4) = -3, take away a rise of 4
becomes (- 3) + (- 4) = -3 plus a drop of 4 degrees
= puts the answer at 7 below zero, or at (- 7)
~ Page 2 ~
b)
(+5) – (-5) = a rise of 5 degrees, take away a drop of 5 degrees
becomes (+5) +(+5) = a rise of 5 degrees plus a rise of 5 degrees
= a rise of 10 degrees or (+10)
Integer Multiplication/Division:
 Multiplication of integers can be seen as repeated addition of a certain number:
5 times +3, 5 X +3, is 5 moves of +3, moving up on the thermometer 5 times., =
+15. The same way, 5 times -3, 5 X -3 is moving down on the thermometer 5
times = -15
 Using the same logic, -5 times -3, -5 X -3,
would give you the opposite of 5 X -3 (-15), or +15.
 So… we can see that when any two integers are being multiplied, if only one of
the numbers has a negative sign in the expression, the result (answer to the
question) becomes negative. If both integers in the expression have negative
signs, the result becomes positive.
 pos. X neg. = neg. neg. X pos. = neg. neg. X neg. = pos.
 These same rules apply to division.
Examples:
Multiplication
- 4 X +5 = -20
Division
-20 divided by +5 = -4,
+20 divided by -5 = -4
+ 3 X -7 = -21
-21 divided by -7 = +3,
-21 divided by +3 = -7
- 2 X -3 = +6
+6 divided by -3 = -2,
+6 divided by -2 = -3
Practice:
a) -7 + -3 = _____
k) +5 - +3 = ______
b) +6 + +2 = _____
l) +8 - ( -2) = ______
c) -8 + -1 = ______
m) -6 - (-7) = ______
d) +9 + +2 = ______
n) +10 - (-5) = ______
e) +7 + - 5 = ______
o) - 17 – (+ 4) = ______
f) -4 + +5 = ______
p) -50 - (-30) = ______
g) +12 + -20 = ______
q) +24 – (-40) = ______
h) -25 + -13 = ______
r) -30 - (+2) = ______
i) -10 + -5 = ______
s) -10 - (10) = ______
j) +14 + -14 = ______
t) +13 – (+5) = ______
a) +4 X +3 = ______
j) +4 div. by -2 = ______
b) -2 X +5 = ______
k) -10 div. by +5 = ______
c) +6 X -3 = ______
l) -6 div. by -3 = ______
d) – 8 X -2 = ______
m) -14 div. by +2 = ______
e) + 4 X -5 = ______
n) +20 div. by -10 = ______
f) -3 X -4 = ______
o) -100 div. by -2 = ______
g) -2 X -3 X -4 = ______
Use order of operations for mixed
expressions:
 Complete Multiplication & Division
in order from Left to Right, then
continue to do the Addition and
Subtraction in order from L to R:
Example:
-12 div. by -3 X -2 = ______
becomes
+4
X -2 = - 8
h) +5 X -3 X -2 = ______
p) -10 div. by -2 X -1 = ______
i) -10 X +2 X -3 = ______
q) +15 div. by -3 X -5 = ______
For multiple number questions,
calculate two at a time:
Example:
-3 X +7 X - 1 = ______
becomes
-21 X -1 = +21
r) - 4 X -8 div. by -2 = ______
Devise your own questions and
answer them on another sheet,
then challenge a partner!
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