# 2.03 Subtraction without regrouping

Lesson

## Ideas

Do you feel you've mastered  subtracting numbers  with up to 4 digits, with no regrouping?

### Examples

#### Example 1

Find the value of 9877-4632.

Worked Solution
Create a strategy

Use the subtraction algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &9 &8 &7 &7 \\ &- & &4 &6 &3 &2 \\ \hline & \\ \hline \end{array}

Subtract the ones column: 7-2=5.

\begin{array}{c} & & &9 &8 &7 &7 \\ &- & &4 &6 &3 &2 \\ \hline & & & & & &5\\ \hline \end{array}

For the tens column, we have 7-3=4:\begin{array}{c} & & &9 &8 &7 &7 \\ &- & &4 &6 &3 &2 \\ \hline & & & & &4 &5\\ \hline \end{array}

In the hundreds column, we have 8-6=2:

\begin{array}{c} & & &9 &8 &7 &7 \\ &- & &4 &6 &3 &2 \\ \hline & & & &2 &4 &5\\ \hline \end{array}

For the thousands place, we have 9 - 4 = 5:\begin{array}{c} & & &9 &8 &7 &7 \\ &- & &4 &6 &3 &2 \\ \hline & & &5 &2 &4 &5\\ \hline \end{array}

So 9877-4632 = 5245.

Idea summary

We can subtract numbers using a vertical algorithm, starting from the units place.

## Subtraction of large numbers

Now we're ready to subtract larger numbers, using a vertical algorithm. Let's see how to do this here.

### Examples

#### Example 2

Find the value of 87\,449-3125.

Worked Solution
Create a strategy

Use the standard algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & \\ \hline \end{array}

Subtract the units column first: 9 - 5= 4.

\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & & & & & &4 \\ \hline \end{array}

Subtract the tens column: 4 - 2 = 2

\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & & & & &2 &4 \\ \hline \end{array}

Subtract the hundreds column: 4 -1 = 3

\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & & & & 3&2 &4 \\ \hline \end{array}

Subtract the thousands column: 7 - 3 = 4

\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & & & 4& 3&2 &4 \\ \hline \end{array}

Subtract the ten thousands column: 8 - 0 = 8

\begin{array}{c} & &8 &7 &4 &4 &9 \\ &- & &3 &1 &2 &5 \\ \hline & & 8& 4& 3&2 &4 \\ \hline \end{array}

So, 87\,449 - 3125 = 84\,324

Idea summary

When subtracting, we always put the number we start with (the total) at the top, and the number we are subtracting, below.