Column Subtraction

What you will learn

• Subtract in columns from the right.
• Exchange from the next place when a digit is too small, including across zeros.
• Check a subtraction by adding.

Before you start: you should be comfortable with Column Addition and Subtracting Within 20.

The idea

The column method for subtraction mirrors addition. Write the bigger number on top and the number you take away underneath, ones under ones. Work from the right.

Exchanging

When the top digit is smaller than the bottom digit in a column, take one from the place to the left and trade it in for ten of the current place. That is called exchange (some people say borrowing).

For $542 - 217$: the ones column needs $2 - 7$. Take $1$ ten from the $4$ tens, leaving $3$ tens. Now the ones column has $12$ ones. $12 - 7 = 5$.

Exchanging across a zero

If the place to the left is a zero, you cannot take one from it. Go one further left, take one from there, and pass it along: the hundred becomes ten tens, then one of the tens becomes ten ones.

Check by adding

Subtraction and addition undo each other. Add your answer to the number you took away: you should get back the top number.

Worked examples

Example 1: One exchange

Work out $732 - 485$.

1. Ones: $2 - 5$ will not work. Exchange: $12 - 5 = 7$. The tens digit $3$ becomes $2$.
2. Tens: $2 - 8$ will not work. Exchange: $12 - 8 = 4$. The hundreds digit $7$ becomes $6$.
3. Hundreds: $6 - 4 = 2$.

Answer: $247$. Check: $247 + 485 = 732$.

Example 2: Across a zero

Work out $5{,}000 - 1{,}234$.

1. Thousands, hundreds and tens are all zero, so exchange one thousand: $4$ thousands, $10$ hundreds. Pass on: $9$ hundreds, $10$ tens. Pass on: $9$ tens, $10$ ones.
2. Ones: $10 - 4 = 6$.
3. Tens: $9 - 3 = 6$.
4. Hundreds: $9 - 2 = 7$.
5. Thousands: $4 - 1 = 3$.

Answer: $3{,}766$. Check: $3766 + 1234 = 5000$.

Example 3: Find the difference

How much taller is a $1{,}340$ m mountain than a $875$ m hill?

1. Subtract: $1340 - 875$.
2. Ones: $0 - 5$, exchange: $10 - 5 = 5$; tens become $3$.
3. Tens: $3 - 7$, exchange: $13 - 7 = 6$; hundreds become $2$.
4. Hundreds: $2 - 8$, exchange: $12 - 8 = 4$; thousands become $0$.

Answer: $465$ m.

Put the bigger number on top. Subtraction is not the same either way round: $5 - 3$ is not $3 - 5$.

Why it matters

Subtraction finds change, differences and how much is left. The column method works for any size of number, and checking by adding is a habit that catches slips before they cost anything.