Hong Kong
Stage 2

# Partitioning Numbers (up to millions)

Lesson

Partitioning large numbers can help us solve number problems, allowing us to work with smaller parts, or chunks. There are many ways in which we can partition a number, so having a collection of ideas can help you when you are solving number problems.

We can break a number down by each digit, or we might break it down into one or two chunks only. The value of each digit, depending on its place value, is also an important way to think of the parts that make up our number. Thinking of digits and whether they represent units, tens, hundreds etc. is a good way to think of how to break numbers into chunks.

You may wish to refresh your memory on how we partitioned numbers to 50 000 and then watch the video here to partition bigger numbers.

In the video, you can see we used a strategy of partitioning our number, to find half of the original number. So, to work out $\frac{1}{2}$12 of $802426$802426, we partitioned it into $800000+2000+400+20+6$800000+2000+400+20+6 and then we calculated half of each separate  part. Adding these separate answers together gave us our final answer.

## The partition-double strategy

What if we used a similar approach, but this time for doubling a number? Well, we can do the same thing!  Let's see how this might work.  Calculate the double of $824$824. First, we partition our number, and then we can double each individual part.

$824=800+20+4$824=800+20+4

Can you write out the next step and solve this number problem? Have a go, and see what your answer is. Then, look right below the questions, and you'll see I've popped the answer there for you.

#### Worked Examples

##### question 1

Fill in the box with the missing number.

1. $3115379=3115300+\editable{}$3115379=3115300+

##### question 2

What is the place value of $3$3 in $8385641$8385641?

1. tens of thousands

A

hundreds of thousands

B

millions

C

tens of millions

D

##### question 3

Use partitioning to fill in the missing number.

1. Use partitioning to complete this number sentence:

$372282$372282$\text{= }$= $370000$370000$\text{+ }$+ $\editable{}$

2. Now use the partitioning and doubling strategy to find the sum:

$372282+370000$372282+370000

Answer to partition-double question

$2\times800+2\times20+2\times4$2×800+2×20+2×4

$=1600+40+8$=1600+40+8

$=1648$=1648