# 4.06 Subtraction with regrouping

Lesson

## Ideas

How confident are you that you can subtract numbers down your page,  using a vertical algorithm  ?

### Examples

#### Example 1

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

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 with regroup

Let's see what we need to do when we don't have enough in one of our place value columns to subtract.

### Examples

#### Example 2

Find the value of 58 - 29.

Worked Solution
Create a strategy

Use the subtraction algorithm with regrouping.

Apply the idea

Write the subtraction in a vertical algorithm.\begin{array}{c} & &5 &8 \\ &- &2 &9 \\ \hline & \\ \hline \end{array}

Begin with the ones column. Since we don't have enough ones to subtract 9 from 8, we need to trade 1 ten from the tens place. \begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & & \\ \hline \end{array}

Now we can subtract 9 from 18 in the ones column and 5 tens becomes 4 tens.\begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & & & 9 \\ \hline \end{array}

Then subtract the numbers in the tens column, 4- 2 = 2.\begin{array}{c} & &4 & \text{}^1 8 \\ &- &2 &9 \\ \hline & &2 & 9 \\ \hline \end{array}

So, 58 - 29=29.

Idea summary

We always start from the ones place, when we work down our page. If we don't have enough ones to subtract, we need to trade from the tens place.

### Outcomes

#### MA2-5NA

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