ADDING, SUBTRACTING WHOLE NUMBERS EASILY

Break Them Up then Add or Subtract Them

A Natural Number is a positive WHOLE NUMBER such as 17, 3, 0 or 247.

An fast way to add and subtract them is to break them up into
sums and/or differences 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 subtract.
For example 150 – 23 can be rewritten 150 – 20 – 3 = 130 3 or 127
because 150 – 20 = 130 and 130 – 3 = 127.

The trick is to use numbers that sum to 5's, 10's and 0's, then add and/or
subtract them in whatever order makes it easy to find mentally.
We use the associative property, that says we can add
and/or subtract in any order as long as we include all the numbers in the question.

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Examples

a) 28 19 = 20 + 8 10 9 = 9

since 20 10 = 10 and 10 + 8 9 = 9

b) 35 + 58 = 30 + 5 + 50 + 5 + 3 = 93

do 30 + 50 + 10 (from the two 5's) + 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) 270 35 h) 49 25

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Solutions

1) Find these sums by the method above. (your numbers may differ from the answers).

a) 17 + 14

10 + 7 + 10 + 4 =
20 + 11 = 31

b) 55 + 16

50 + 5 + 10 + 6 =
60 + 11 = 71

c) 93 + 18

90 + 3 + 10 + 8 =
100 + 11 = 111

d) 84 + 17

80 + 4 + 10 + 7 =
90 + 11 = 101

       
e) 74 + 25

70 + 4 + 20 + 5 =
90 + 9 = 99

f) 55 + 36

50 + 5 + 30 + 6 =
80 + 11 = 91

g) 27 + 35

20 + 7 + 30 + 5 =
50 + 12 = 62

h) 49 + 25

40 + 9 + 20 + 5 =
60 + 14 = 74

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

a) 60 12

60 10 2 = 48

b) 55 16

50 + 5 10 6 =
45
6 = 39

c) 97 18

90 + 7 10 8 =
80 8 + 7 = 79

d) 84 17

80 + 4 10 7 =
70 7 + 4 = 67

       
e) 74 25

75 1 25 =
50 1 = 49

f) 55 36

50 + 5 30 6 =
20 + 5 6 = 19

g) 270 35

270 30 5 = 235

h) 49 25

50 1 25 =
25 1 = 24

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