# 2.05 Subtraction with regrouping

Lesson

## Ideas

When we add numbers together, place value is really important. Do you remember how to  add numbers with three or more digits  together?

### Examples

#### Example 1

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

a

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

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

b

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

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

c

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.

Idea summary

Addition by partitioning involves splitting numbers into each place value. The place values are then added separately.

## Subtraction with regrouping

When we subtract, we may need to regroup, or trade, some of our numbers. This video shows how we can do that, so that we can subtract another number. Let's take a look.

### Examples

#### Example 2

Find the value of 355-237.

Worked Solution
Create a strategy

Use the subtraction algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &3 &5 &5 \\ &- & &2 &3 &7 \\ \hline & \\ \hline \end{array}

Begin with the units column. We can see that 5 is less than 7, so we need to trade 1 ten from the tens place.

So we get 15-7=8 in the units column and 5 tens becomes 4 tens in the first row.\begin{array}{c} & & &3 &4 &\text{}^1 5 \\ &- & &2 &3 &7 \\ \hline & & & & &8 \\ \hline \end{array}

For the tens place: 4-3=1. \begin{array}{c} & & &3 &4 &\text{}^1 5 \\ &- & &2 &3 &7 \\ \hline & & & &1 &8 \\ \hline \end{array}

For the hundreds place: 3-2=1.

\begin{array}{c} & & &3 &4 &\text{}^1 5 \\ &- & &2 &3 &7 \\ \hline & & &1 &1 &8 \\ \hline \end{array}

So 355-137 = 118.

Idea summary

We always start from the ones place, when we work in a vertical algorithm. If we don't have enough to subtract, we can regroup from the next place to the left.

## Subtract larger numbers

This time we have numbers with more digits, and the video shows how we can trade, or regroup, thousands to help us subtract in the hundreds place.

### Examples

#### Example 3

Find the value of 6241-2319.

Worked Solution
Create a strategy

Use the subtraction algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &6 &2 &4 &1 \\ &- & &2 &3 &1 &9 \\ \hline & \\ \hline \end{array}

In the units column we can see that 1 is less than 9, so we need to trade 1 ten from the tens column. This gives us 11-9=2 in the units column and 4 tens becomes 3 tens in the first row.\begin{array}{c} & & &6 &2 &3 &\text{}^1 1 \\ &- & &2 &3 &1 &9 \\ \hline & & & & & &2 \\ \hline \end{array}

For the tens column we have 3-1=2: \begin{array}{c} & & &6 &2 &3 &\text{}^1 1 \\ &- & &2 &3 &1 &9 \\ \hline & & & & &2 &2 \\ \hline \end{array}

In the hundreds column we can see that 2 is less than 3, so we need to trade 1 thousand from the thousands column. This gives us 12-3=9 and and 6 thousands becomes 5 thousands in the first row.\begin{array}{c} & & &5 &\text{}^1 2 &3 &\text{}^1 1 \\ &- & &2 &3 &1 &9 \\ \hline & & & &9 &2 &2 \\ \hline \end{array}

For the thousands column we have 5-2=3:\begin{array}{c} & & &5 &\text{}^1 2 &3 &\text{}^1 1 \\ &- & &2 &3 &1 &9 \\ \hline & & &3 &9 &2 &2 \\ \hline \end{array}

So 6241-2319=3922.

Idea summary

If we don't have enough to subtract, we can regroup from the next place to the left.

### Outcomes

#### MA2-5NA

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