Partitioning to Add

What is partitioning?

Partitioning means splitting a number into its parts. The most useful way to split a two-digit number is into its tens and its ones.

• 47 partitions into 40 and 7.
• 25 partitions into 20 and 5.
• 63 partitions into 60 and 3.

This works because of place value: the first digit tells you how many tens, the second tells you how many ones. If place value is still settling, our lesson on place value: tens and ones explains it carefully.

Adding by partitioning

To add two numbers, partition both, add the tens to the tens and the ones to the ones, then recombine.

Take 34 + 25:

1. Partition: 34 = 30 + 4, and 25 = 20 + 5.
2. Add the tens: 30 + 20 = 50.
3. Add the ones: 4 + 5 = 9.
4. Recombine: 50 + 9 = 59.

So 34 + 25 = 59.

Why keep tens with tens? Because tens and ones are different sizes — like keeping pound coins separate from pennies. You count each kind, then add the totals together at the end.

Following the steps in a table

Sum	Tens + tens	Ones + ones	Recombine	Total
34 + 25	30 + 20 = 50	4 + 5 = 9	50 + 9	59
52 + 36	50 + 30 = 80	2 + 6 = 8	80 + 8	88
41 + 27	40 + 20 = 60	1 + 7 = 8	60 + 8	68
28 + 35	20 + 30 = 50	8 + 5 = 13	50 + 13	63

Worked example 1: no extra ten

Work out 52 + 36.

1. 52 = 50 + 2, and 36 = 30 + 6.
2. Tens: 50 + 30 = 80.
3. Ones: 2 + 6 = 8.
4. Recombine: 80 + 8 = 88.

So 52 + 36 = 88.

Worked example 2: when the ones make more than ten

Work out 28 + 35. Watch the ones carefully.

1. 28 = 20 + 8, and 35 = 30 + 5.
2. Tens: 20 + 30 = 50.
3. Ones: 8 + 5 = 13 — that is more than ten!
4. Recombine: 50 + 13 = 63.

The ones made an extra ten, which simply joins the other tens when you recombine. So 28 + 35 = 63.

Worked example 3: partitioning just one number

Sometimes it is quicker to partition only the second number and add it in two jumps. Work out 46 + 23:

1. Partition 23 into 20 and 3.
2. Add the tens first: 46 + 20 = 66.
3. Then add the ones: 66 + 3 = 69.

So 46 + 23 = 69. This jump method is handy for adding mentally.

Why this strategy matters

Partitioning shows you what is really happening when you add: you are combining tens with tens and ones with ones. That understanding is exactly the thinking behind written column addition — the columns just line up the parts for you. Master partitioning now and the formal method will make complete sense later, instead of feeling like a magic recipe.

Try it yourself

You will need base-ten blocks, or draw tens as sticks and ones as dots.

1. Build two numbers, like 34 and 25, with sticks and dots.
2. Push all the tens sticks together and count them.
3. Push all the ones dots together and count them.
4. If you have ten or more dots, swap ten dots for one stick.
5. Read off the total and say it aloud. Challenge: Pick sums where the ones cross ten, like 27 + 18.

What's next?

Partitioning is the bridge to written methods. See how the columns work in column addition with carrying, and speed up your mental adding with mental math strategies.