Tiffany likes maths and loves to learn how to calculate. She likes to wear her numbers dress when she is learning maths.

Tiffany has been learning about partitioning.

**Did you know?**

Partitioning means breaking a number up into smaller parts to make calculations easier.

Partitioning is sometimes called chunking.

You need to understand place value to be able to partition numbers.

### How to partition numbers

Partitioning means breaking larger numbers into smaller chunks, separating ones, tens, hundreds, thousands etc., to make calculations easier.

For example:

Using place value we know that the number 45 is made up of four tens and 5 ones.

45 = 40 + 5

The number 126 is made up of one hundred, two tens and six ones

126 = 100 + 20 + 6

Looking at the place value for the number 1253 we know that this number has one thousand, two hundreds, five tens and three ones.

1253 = 1000 + 200 + 50 + 3

### Adding numbers by partitioning

Example 1:

53 + 26 = ?

53 can be partitioned to 50 + 3 and 26 can be partitioned to 20 + 6

Add the tens together 50 + 20 = 70

Add the ones together 3 + 6 = 9

70 + 9 = 79

53 + 26 = 79

Example 2:

158 + 194 = ?

158 can be partitioned to 100 + 50 + 8 and 194 can be partitioned to 100 + 90 + 4

add the hundreds together 100 + 100 = 200

add the tens together 50 + 90 = 140

add the ones together 8 + 4 = 12

200 + 140 + 12 = 352

158 + 194 = 352

### Subtracting numbers by partitioning

Example 1:

56 – 23 = ?

56 can be partitioned to 50 + 6 and 23 can be partitioned to 20 + 3

Subtract the ones then subtract the tens

Add the two answers together

Example 2:

our sum is

158 – 134 =

158 can be partitioned to 100 + 50 + 8 and 134 can be partitioned to 100 + 30 + 4

Subtract the ones, then the tens, then the hundreds

Add the answers together

### Subtracting using partitioning and exchanging/regrouping

Example:

242 – 128 = ?

242 can be partitioned to 200 + 40 + 2 and 128 can be partitioned to 100 + 20 + 8

Subtract the ones first, then the tens, then the hundreds

We need to subtract the ones first but we cannot take 8 away from 2

In order to complete the calculation we have to do an exchange and take one ten from the tens column and add it to the ones column.

We can now complete the calculation

Tiffany has enjoyed learning about partitioning. She summed up her learning with the following keywords:

adding, answer, chunking, exchanging, hundreds, ones, partitioning, place value, regrouping, subtracting, tens, thousands