# 3.05 Addition using algorithm

Lesson

## Are you ready?

Do you remember how we can  break numbers into place value parts  ?

### Examples

#### Example 1

We have written a number in the number expander below.

a

What is the value of the units?

Worked Solution
Create a strategy

Multiply the number of units by 1.

Apply the idea

The number expander above, says there are 2 units.

So the value of the units is 2 \times 1 = 2.

b

What is the value of the tens?

Worked Solution
Create a strategy

Multiply the number of tens by 10.

Apply the idea

The number expander says there are 3 tens.

So the value of the tens is 30.

c

Now look at the number 67. What is the value of the tens?

Worked Solution
Create a strategy

Use a number expander with tens and units.

Apply the idea

Using the number expander, break 67 into tens and units.

So we have

So the value of the tens is 60.

Idea summary

A number expander can help us find the values of the digits of a number.

## Addition algorithm

We are going to use place value to add numbers together, working down our page. This is called using an algorithm.

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### Examples

#### Example 2

Find the value of 41 + 56.

Worked Solution
Create a strategy

Use the addition algorithm.

Apply the idea

Write the addition in a vertical algorithm.\begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline & \\ \hline \end{array}

Add the smallest place value first. So 1 + 6 = 7. \begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline & & &7 \\ \hline \end{array}

Then add the next place value. 4 + 5 = 9. \begin{array}{c} & &4 &1 \\ &+ &5 &6 \\ \hline & &9 &7 \\ \hline \end{array}

So 41 + 56 = 97.

Idea summary

When we add this way, we always start at the place value that is farthest to the right, which is the units place. This helps if we have to regroup to the next place.

### Outcomes

#### MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers