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.

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Examples

Example 2

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

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

Hundreds	Tens	Ones
7	0	5
7	0	0

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

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

Hundreds	Tens	Ones
2	0	5
		5

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

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.

\displaystyle 705 + 205	\displaystyle =	\displaystyle 700 + 5 + 200 + 5	Use the partitions
	\displaystyle =	\displaystyle 700 + 200 + 5 + 5	Group the hundreds and ones
	\displaystyle =	\displaystyle 900 + 10	Add the hundreds and ones
	\displaystyle =	\displaystyle 910

705 + 205 = 910

Idea summary

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

Addition of large numbers

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

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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

ACMNA123

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

ACMNA127

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies

ACMNA132

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies

2.01 Addition

Ideas

Are you ready?

Examples

Example 1

Addition by place value

Examples

Example 2

Addition of large numbers

Examples

Example 3

Outcomes

ACMNA123

ACMNA127

ACMNA132

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