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## Subtraction

### All Positive

Subtracting one decimal from the other is similar to addition.

Two positive decimal numbers may be subtracted as follows:

• the numbers are written one below the other with the decimal points vertically aligned
• mentally place a zero in any places where only one of the numbers has a digit.
• the numbers are subtracted as if they are whole numbers
• a decimal point is placed in the difference such that it is directly below the decimal points in the numbers being subtracted

To begin with given are examples where the numbers being subtracted are positive and the answer will be positive.

### Example

Let us calculate:   123.45 - 37.5 ### Example

 −      =

### Exercise

Perform the following subtractions without using a calculator:

 .   −    . .

### Small positive number minus large positive number

Subtracting a large number from a small number will always give a negative number, the opposite of subracting the small number from the large number.

This can be written:  ab = −(ba)

### Example

Calculate 11.6 − 18.0 without using a calcuator.

This is the opposite of 18.0 − 11.6 which equals 6.4.

Hence 11.6 − 18.0 = −6.4

### Exercise

Perform the following subtractions without using a calculator:

 .   −    . .

### Subtracting Signed Decimal Numbers

This section assumes you are already familiar with subtraction for integers. The things to remember are summarised here.

• Subtraction of a number is equivalent to adding its negative. That is:
xy = x + (−y) for any numbers x and y.
• Subtracting a negative number is equivalent to adding its positive. That is,
x − (−y) = x + y

### Examples

We show application of these rules to signed decimal numbers.

(3.1) − (−3.3) = 3.1 + 3.3 = 6.4

(−3.1) − (−3.3) = (−3.1) + (3.3) = 0.2

(3.1) − (3.3) = −(3.3 − 3.1) = −0.2

(−3.1) − (3.3) = (−3.1) + (−3.3) = −6.4

### Exercise

Try these exercises with signed decimal numbers without using a calculator.

 .   −    . .

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