+ and – signs have two uses in arithmetic

- As number signs
- As arithmetic operation signs

**+ and – as Number Signs**

As number signs, + and – are used to represent opposites. See one of my previous articles in this blog to read more about negative numbers as opposites.

As number signs, – and + are written just before a number. All numbers except zero are either positive or negative.

– sign indicates that a number is negative

–2 is 2 less than zero

+ sign or no sign show that a number is positive

+2 is 2 more than zero

2 is 2 more than zero

Any two exact opposites nullify each other to give a zero sum

–3 + 3 = 0

–8 + 8 = 0

**+ and – as Arithmetic Operation Signs**

As operation signs, + is the sign of addition while – is the sign of subtraction. Addition and subtraction involve more than one number. So addition and subtraction signs are not associated with numbers but are written between them.

0 + (+3) or 0 + 3 means increase 0 by 3 which gives 3

– 2 – (+3) or – 2 – 3 means decrease – 2 by 3 which gives –5

**Example 1**

Temperature of a place was –5°C in morning. It rose to 10°C by noon and fell again to 2°C by evening. What is the change in temperature from morning to noon and from noon to evening?

**Solution**

The temperature first rose from –5°C in morning to 0°C and then to 10°C in noon. Rise from –5°C to 0°C is 5°C. From 0°C to 10°C, the rise is 10°C. So the total rise from morning to noon is 15°C**. **It may also be stated as a change of +15°C from morning to noon.

The temperature falls from 10°C in noon to 2°C in evening. This is a fall of 8°C from noon to evening. It may also be said that temperature changes by –8°C from noon to evening.

Combining much related uses of + and – signs facilitate addition and subtraction of directed numbers. The two uses are closely related and work well together in carrying out calculations with numbers. 0 – 2 is same as –2 although sign changes its role from being one of subtraction to a number sign.

Consider the interplay of signs between two numbers in the example below. This emphasizes the relationship between number and operation signs.

**Example 2**

Calculate the result of 2 + (–4).

**Solution**

The given example 2 + (–4) says increase 2 by –4. This may seem strange and weird. The expression 2 – (+4) or simply 2 – 4 is straightforward. It simply requires a decrease in 2 by 4.

Two is required to be increased by the opposite of 4. –4 is 4 less than zero. Opposites give a zero sum 4 + (–4) = 0. So 2 + (–4) is an indirect way of expressing a decrease of 2 by 4. So 2 + (–4) is same as 2 – (+4). Thus

2 + (–4) = –2

Applying your learning to simple real world situations will be of great help to appreciate uses of these signs and how they work together. Many word problems are available on the internet and in books.

Think your own new simple real world situations involving uses of these signs. Then find solutions to them verbally in your head. Short solutions may be practiced this way.

It may be helpful if you use brackets to differentiate number from operation signs when they come next to each other.

Think then rethink about these signs and their applications. Math is subtle and is appreciated this way. A study group can be very helpful for such activity.