# 4.05 Subtraction using algorithm

Lesson

## Ideas

How did you find  adding numbers, using the standard algorithm  ?

### Examples

#### Example 1

Find the value of 41 + 56.

Worked Solution
Create a strategy

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

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.

## Subtraction without regrouping

Let's try some subtraction problems, using the standard algorithm. We use place value models to help us, so you might like to have some handy as you watch the video.

### Examples

#### Example 2

Find the value of 95 -51.

Worked Solution
Create a strategy

Use the subtraction algorithm.

Apply the idea

Write the subtraction in a vertical algorithm.\begin{array}{c} & &9 &5 \\ &- &5 &1 \\ \hline & \\ \hline \end{array}

Subtract the smallest place value first. So 5 - 1 = 4.\begin{array}{c} & &9 &5 \\ &- &5 &1 \\ \hline & & &4 \\ \hline \end{array}

Then subtract the next place value, 9- 5 = 4.\begin{array}{c} & &9 &5 \\ &- &5 &1 \\ \hline & &4 &4 \\ \hline \end{array}

So, 95- 51 = 44.

Idea summary

When we solve problems using an algorithm, we have to line up our digits by place value. With subtraction, we always put the total at the top, and the number we are subtracting, below.

### Outcomes

#### MA2-5NA

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