Decomposing
Decomposing numbers allows children to perform more complex addition and subtraction problems with ease. Decomposition requires children to have a sound understanding of the place value of numbers (hundreds, tens and units). Here are a few examples to explain the processes involved.
Decomposing tens and units
1 ten is the same as 10 units
1 hundred is the same as 10 tens or 100 units
240 is 2 hundreds and 4 tens or 24 tens
357 is 3 hundreds, 5 tens and 7 units or 35 tens and 7 units
This can be altered to help solve subtraction problems
e.g. 357 can be 3 hundreds, 4 tens and 17 units
or 2 hundreds, 15 tens and 7 units1 ten is the same as 10 units
Horizontal addition
2 digits
67 + 24 = (60+20) + (7+4) = 80+11 = 91
3 digits
231 + 126 = (200 + 100) + (30+20) + (1+6)
= ( 300 ) + ( 50 ) + ( 7 )
= 357
Horizontal subtraction
2 digits
74 - 31 = (70 - 30) + (4 - 1) = 40 + 3 = 43
3 digits
569 - 132 = (500 - 100) + (60 - 30) + (9 - 2)
= ( 400 ) + ( 30 ) + ( 7 )
= 437
Vertical addition
2 digits
47
+ 76
110
13
123
3 digits
368
+ 493
700
150
11
861
Subtraction
2 digits
81 – 57 =
81 = 80 + 1 = 70 + 11
- 57 = 50 + 7 50 + 7
20 + 4 = 24
3 digits
563 – 258 =
500 + 60 + 3 500 + 50 + 13
- 200 + 50 + 8 - 200 + 50 + 8
300 + 0 + 5 = 305
3 digits – decomposing hundreds into tens
569 – 278 =
500 + 60 + 9 400 + 160 + 9
- 200 + 70 + 8 - 200 + 70 + 8
200 + 90 + 1 = 291
3 digits – decomposing hundreds into tens and then tens into ones
566 – 278 =
(decomposing the hundreds)
500 + 60 + 6 400 + 160 + 6
- 200 + 70 + 8 - 200 + 70 + 8
(decomposing the tens)
400 + 150 + 16
- 200 + 70 + 8
200 + 80 + 8 = 288