 Lesson

## Ideas

Breaking up numbers into parts, often by place value, can help with addition. Do you know how to  partition a number by place value?

### Examples

#### Example 1

We're going to write 56\,713 in expanded form.

a

Fill in the number expander for 56\,713.

56\,713=⬚ \, \text{ Ten-Thousands }⬚ \, \text{ Thousands }⬚ \, \text{ Hundreds }⬚ \, \text{ Tens }⬚ \, \text{ Units}

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

56\,713=5 \, \text{ Ten-Thousands }6 \, \text{ Thousands }7 \, \text{ Hundreds }1 \, \text{ Tens }3 \, \text{ Units}

b

56\,713=⬚+⬚+⬚+10+3

Worked Solution
Create a strategy

Use the number expander in part (a).

Apply the idea

5 is in ten thousands, 6 is in thousands, and 7 is in hundreds, so the values are 50\,000, 6000, and 700.

56\,713=50\,000+6000+700+10+3

Idea summary

We can use a place value table to write numbers in expanded form.

Place value is something we need to know when solving addition, whether working across our page, or using a vertical algorithm. Let's see how it helps us, including regrouping.

### Examples

#### Example 2

Let's find the value of 705 + 205, by partitioning the numbers.

a

Fill in the box with the missing number.

705 = 700 + ⬚

Worked Solution
Create a strategy

Put the numbers in a place value table.

Apply the idea

The only place where that the two numbers differ is in the units column. The first number has 5 units where as the second number has 0 units.

So we need to add 5 more to the number 700 to equal 705.

705 = 700 + 5

b

Fill in the box with the missing number.

205 = ⬚ + 5

Worked Solution
Create a strategy

Put the numbers in a place value table.

Apply the idea

In the place value table, both 205 and 5 have 5 units but they don't match up in the tens and hundreds columns.

So we need to add 0 tens and 2 hundreds or 200 to 5 to get 205.

205 = 200 + 5

c

Find the value of 705 + 205.

Worked Solution
Create a strategy

Add the partitions of the two numbers.

Apply the idea

In parts (a) and (b), we have the partitions of these two numbers:

705 = 700 + 5 \\ 205 = 200 + 5

We can use these to add the two numbers.

705 + 205 = 910

Idea summary

To add large numbers, we can first partition the numbers and then add their partitions.

We can use vertical algorithms to work with larger numbers as well, as we do in this video.

### Examples

#### Example 3

Find the value of 19\,292 + 34\,131.

Worked Solution
Create a strategy

Use the standard algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &1 &9 &2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & \\ \hline \end{array}

Add the units column first.\begin{array}{c} & & &1 &9 &2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & & & &3\\ \hline \end{array}

In the tens column we get 9+3=12. So we bring down 2 and carry the 1 to the hundreds place.\begin{array}{c} & & &1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & & &2 &3\\ \hline \end{array}

In the hundreds column we get 1+2+1=4.\begin{array}{c} & & &1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & &4 &2 &3\\ \hline \end{array}

In the thousands column we get 9 + 4 = 13. So we bring down 3 and carry the 1 to the ten thousands place.\begin{array}{c} & & &\text{}^1 1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & & 3&4 &2 &3\\ \hline \end{array}

For the ten thousands place we get 1+1+3=5.\begin{array}{c} & & &\text{}^1 1 &9 &\text{}^ 1 2 &9 &2 \\ &+ & &3 &4 &1 &3 &1 \\ \hline & & & 5& 3&4 &2 &3\\ \hline \end{array}

So the answer is:19\,292 + 34\,131 = 53\,423

Idea summary

We often call on different methods when we solve addition problems, so remember to use things such as:

• bridge (build) to 10

• partitioning numbers

• number lines

• place value

• vertical algorithms

### Outcomes

#### VCMNA209

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations