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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