Add the numbers down each column starting from the ones column, then the tens column to get:\begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline & &9 &7 \\ \hline \end{array}So 41 + 56 = 97.

Idea summary

You might notice that sometimes the standard algorithm is called the 'vertical algorithm'. Let's think about why. When we use the standard algorithm, we line our numbers up in 'vertical' place value columns.

Addition with place value models and the number line

Let's see how place value models (also called Base 10 models) can help us with adding numbers together.

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We can also use a number line to help with addition, so let's see how we solve the same problem, 321 + 243, using a number line this time.

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Examples

Example 2

Use the number line, to help you find the value of 19 + 343.

Worked Solution

Create a strategy

Start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 343 is.

Jump 19 units to the right from 343.

We end up at the number 362. So: 19 + 343 = 362

Idea summary

When we add on a number line, we move to the right. It is usually easiest to start with the larger number and add the smaller number.

Addition with place value columns

This time we add some 4-digit numbers, using place value columns.

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Examples

Example 3

Find the value of 4400 + 403.

Worked Solution

Create a strategy

Use the vertical algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline \\ \hline \end{array}

Add the units column first: 0 + 3 = 3.

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & & & &3\\ \hline \end{array}

Add the tens column: 0 + 0 = 0

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & & &0 &3\\ \hline \end{array}

Add the hundreds column: 4 + 4 = 8

\begin{array}{c} & &4 &4 &0 &0 \\ &+ & &4 &0 &3 \\ \hline & & &8 &0 &3\\ \hline \end{array}

Add the thousands column: 4 + 0 = 4

\begin{array}{c} & &4 &4&0 &0 \\ &+ & &4 &0 &3 \\ \hline & &4 &8 &0 &3\\ \hline \end{array}

4400 + 403 = 4803

Idea summary

There are different ways to solve addition problems, and you can use them to add numbers of different sizes. It doesn't matter if your number has 3 digits, 4 digits, or even more.

Outcomes

ACMNA073

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ACMNA076

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

2.02 Addition without regrouping

Ideas

Are you ready?

Examples

Example 1

Addition with place value models and the number line

Examples

Example 2

Addition with place value columns

Examples

Example 3

Outcomes

ACMNA073

ACMNA076

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