ADDING INTEGERS EASILY 
An Integer is a positive or negative WHOLE NUMBER such as 17, 3, – 9 or – 24.
An easy way to add integers is to break the numbers up into sums that are easy to find.
For example, say we have to add 22 + 17.
If we rewrite it as 20 + 2 + 10 + 7, it's obvious the sum = 39.
This technique works especially well when we add negative numbers or subtract.
For example 15 + (– 23) can be rewritten 15 + (– 20) + (– 3) = (–5) + (– 3) or – 8,
because 15 + (– 20) = – 5.
Another approach to this question is to turn the sum around using the commutative property.
We now have
(– 23) + 15 = (– 15) + (– 5) + (– 3) + 15 = – 8
because the "15's" cancel each other out.
The trick is to use numbers that sum to 5's, 10's and zeros to make it easy to find mentally.
Examples
a) (28) + (– 19) = 20 + 8 – 10 – 9 = 9 since 20 – 10 = 10 and 8 – 9 = –1 
b) (35) + (58) = 30 + 5 + 50 + 5 + 3 = 93 do 30 + 50 + 10 + 3 
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Practice
1) Find these sums by the method above. (your numbers may differ from mine).
a) 17 + 14  b) 55 + 16  c) 93 + 18  d) 84 + 17 
e) 74 + 25  f) 55 + 36  g) 27 + 35  h) 49 + 25 
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2) Find these differences by the method above. (your numbers may differ from mine).
a) 60 – 12  b) 55 – 16  c) 97 – 18  d) 84 – 17 
e) 74 – 25  f) 55 – 36  g) 27 – 35  h) 49 – 25 
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Solutions
1) Find these sums by the method above. (your numbers may differ from mine).
a) 17 + 14 10 + 7 + 10 + 4 = 31 
b) 55 + 16 50 + 5 + 10 + 6 = 71 
c) 93 + 18 90 + 3 + 10 + 8 = 111 
d) 84 + 17 80 + 4 + 10 + 7 = 101 
e) 74 + 25 70 + 4 + 20 + 5 = 99 
f) 55 + 36 50 + 5 + 30 + 6 = 91 
g) 27 + 35 20 + 7 + 30 + 5 = 62 
h) 49 + 25 40 + 9 + 20 + 5 = 74 
2) Find these differences by the method above. (your numbers may differ from mine).
a) 60 – 12 60 – 10 – 2 = 48 
b) 55 – 16 50 + 5 – 10 – 6 = 39 
c) 97 – 18 90 + 7 – 10 – 8 = 79 
d) 84 – 17 80 + 4 – 10 – 7 = 67 
e) 74 – 25 75 – 1 – 25 = 49 
f) 55 – 36 50 + 5 – 30 – 6 = 19 
g) 27 – 35 20 + 7 – 30 – 5 = –8 
h) 49 – 25 50 – 1 – 25 = 24

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