# 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

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

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