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 = 9since 20 – 10 = 10 and 8 – 9 = –1 b) (35) + (58) = 30 + 5 + 50 + 5 + 3 = 93do 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 + 1410 + 7 + 10 + 4 = 31 b) 55 + 1650 + 5 + 10 + 6 = 71 c) 93 + 1890 + 3 + 10 + 8 = 111 d) 84 + 1780 + 4 + 10 + 7 = 101 e) 74 + 2570 + 4 + 20 + 5 = 99 f) 55 + 3650 + 5 + 30 + 6 = 91 g) 27 + 3520 + 7 + 30 + 5 = 62 h) 49 + 2540 + 9 + 20 + 5 = 74

2) Find these differences by the method above. (your numbers may differ from mine).

 a) 60 – 1260 – 10 – 2 = 48 b) 55 – 1650 + 5 – 10 – 6 = 39 c) 97 – 1890 + 7 – 10 – 8 = 79 d) 84 – 1780 + 4 – 10 – 7 = 67 e) 74 – 2575 – 1 – 25 = 49 f) 55 – 3650 + 5 – 30 – 6 = 19 g) 27 – 3520 + 7 – 30 – 5 = –8 h) 49 – 2550 – 1 – 25 = 24

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