MENTAL MATH COMPLEMENTS OF NUMBERS
Two numbers that add together are called complements.
- 12 and 8 are complements to 20 because 12 + 8 = 20
- 35 and 65 are complements to 100 because 35 + 65 = 100
Like this, we can get many combinations.
Loop the complements in each set
Problem 1 :
Complements to 20. There are three to find. The first one has been done is shown.
Solution :
The other two complements of 20 are,
12 + 8 = 20
14 + 6 = 20
Problem 2 :
Complements of 50. There are 8 to find.
Solution :
26 + 24 = 50
17 + 33 = 50
12 + 38 = 50
45 + 5 = 50
18 + 32 = 50
40 + 10 = 50
15 + 35 = 50
30 + 20 = 50
Problem 3 :
Solution :
From the top towards clockwise rotation,
50 - 10 = 40
50 - 20 = 30
50 - 25 = 25
50 - ? = 35,
then ? will be 35 and ? will be complements of 50. So, ? will be 15.
50 - 30 = 20
50 - ? = 15
Here ? and 15 are complements of 50. Then ? will be 35.
50 - 5 = 45
50 - 26 = 24
Problem 4 :
Solution :
100 - 50 = 50
100 - 30 = 70
100 - 90 = 10
100 - ? = 25
then ? and 25 will be complements of 100. So, ? will be 75.
100 - 20 = 80
100 - ? = 75
? and 75 will be complements of 100. So, ? will be 25.
100 - 15 = 85
100 - 60 = 40
Problem 5 :
Show how knowing the complements to 20, 50 and 100 makes adding easier. You may want to loop the complements first.
a) 80 + 20 + 15 + 5 = _____
b) 18 + 2 + 30 + 20 + 10 + 10 = ___
c) 25 + 25 + 40 + 30 + 20 + 10 = _____
d) 15 + 35 + 20 + 30 + 10 + 12 = _____
Solution :
a) 80 + 20 + 15 + 5 =
Using parenthesis, we can group to isolate 20, 50 and 100 complements.
= (80 + 20) + (15 + 5)
= 100 + 20
= 120
So, the answer is 120.
b) 18 + 2 + 30 + 20 + 10 + 10 = ___
= (18 + 2) + (30 + 20) + (10 + 10)
= 20 + 50 + 20
= 90
So, the answer is 90.
c) 25 + 25 + 40 + 30 + 20 + 10 = _____
= (25 + 25) + (40 + 10) + (30 + 20)
= 50 + 50 + 50
= 150
d) 15 + 35 + 20 + 30 + 10 + 12 = _____
= (15 + 35) + (20 + 30) + (10 + 10) + 2
12 is being decomposed as 10 + 2
= 50 + 50 + 20 + 2
= 100 + 20 + 2
= 122
So, 122 is the answer.
Problem 6 :
Complete the complements of 50
|
a) __ + 38 = 50 b) 25 + __ = 50 c) __ + 46 = 50 d) 14 + ___= 50 |
e) __ + 17 = 50 f) 32 + ___ = 50 g) __ + 28 = 50 h) 7 + ___ = 50 |
Solution :
|
a) 12 + 38 = 50 b) 25 + 25 = 50 c) 4 + 46 = 50 d) 14 + 36 = 50 |
e) 33 + 17 = 50 f) 32 + 28 = 50 g) 22 + 28 = 50 h) 7 + 43 = 50 |
Problem 7 :
Complete the complements of 100.
|
a) __ + 54 = 100 b) __ + 46 = 100 c) 62 + ___ = 100 d) 45 + ___= 100 |
e) __ + 22 = 100 f) 33 + ___ = 100 g) 25 + ___ = 100 h) ___ + 48 = 100 |
Solution :
|
a) 46 + 54 = 100 b) 54 + 46 = 100 c) 62 + 38 = 100 d) 45 + 55 = 100 |
e) 78 + 22 = 100 f) 33 + 67 = 100 g) 25 + 75 = 100 h) 52 + 48 = 100 |
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