# 1.03 Partition numbers

Lesson

## Ideas

Before we look at breaking up 6 digit numbers, check if you remember how it worked with smaller numbers.

### Examples

#### Example 1

Fill in the box with the missing number.

2476=2000+⬚

Worked Solution
Create a strategy

Put the first number in a place value table.

Apply the idea

The 2 in the thousands column is equal to 2000. So we need to add the rest of the digits which make the number 476.

2476=2000+476

Idea summary

Place value tables are useful in breaking up numbers.

## Partition numbers up to one million

Let's see how we can partition a number in the hundreds of thousands, and then how to partition a number slightly differently, to solve a division problem.

### Exploration

Enter a 7 digit number to see the value of each digit.

Any 7 digit number can be expanded into millions, hundred thousands, ten thousands, thousands, hundreds, tens, and units.

### Examples

#### Example 2

Fill in the boxes with the missing numbers.

8\,555\,777=⬚+500\,000+50\,000+⬚+700+70+⬚

Worked Solution
Create a strategy

Put the number on the left in a place value table.

Apply the idea

8\,555\,777=8\,000\,000+500\,000+50\,000+5000+700+70+7

#### Example 3

a

Write the number that is made up of 10 ten thousands, 10 hundreds and 3 tens.

Worked Solution
Create a strategy

Put the number in a place value table.

Apply the idea

We use the following facts: \begin{aligned}10 \text{ ten thousands} &= 1 \text{ hundred thousand} \\ 10 \text{ hundreds} &= 1 \text{ thousand} \end{aligned}

The number that is made up of 10 ten thousands, 10 hundreds and 3 tens is 101\,030

b

Write the number that is made up of 6 hundred thousands, 10 tens and 2 ones.

Worked Solution
Create a strategy

Put the number in a place value table.

Apply the idea

We use the fact that 10 tens is equal to 1 hundred and put it in the place value table.

The number that is made up of 6 hundred thousands, 10 tens and 2 ones is 600\,102

Idea summary

Partitioning by place value is really useful, but sometimes breaking up a number into other parts is a great way to help solve problems.

### Outcomes

#### MA3-4NA

orders, reads and represents integers of any size and describes properties of whole numbers