Arithmetic » Negative numbers & greater than and less than  


Contents

1. What is a negative number?
2. Greater than and less than
3. Adding and subtracting negative numbers
4. Multiplying and dividing negative numbers

1. What is a negative number?

Negative numbers are used for example with temperatures.
Below 0 °C it will start freezing and we use –1 °C, –2 °C, et cetera.
Image of thermometers, positive is above zero, negative is less than zero, zero is neutral

Neutral

The number 0 is neither positive nor negative, but neutral.

In Belgium and France however, this is not the case.
They find zero and positive and negative.
Numbers above zero, they call 'purely' positive and numbers below zero 'purely' negative.

Opposite

Positive and negative numbers are each others opposite.
The opposite of 3 is –3.
The opposite of –7 is 7.

2. Greater than and less than

On the number line the negative numbers are to the left of zero.
The more left the number, the smaller the number. Number line from small left to big right

–5 is less than 4, because –5 lies to the left of 4 on the number line.
–1 is greater than –3, because –1 lies to the right of –3 on the number line.

For less than you can use the <-sign.
For greater than you can use the >-sign.

Mnemonics are:
1. The direction of < and > always points towards the smallest number.
2. The < and > sign bites towards the biggest number.
3. You can change < into a K of "kleiner dan" (for Dutch students).

3. Adding and subtracting negative numbers

Remember this:
+ – is the same as –
– – is the same as +

Examples

5 + 7 = 12
5 + –7 = 5 – 7= –2 (you add –7 to 5)
5 – –7 = 5 + 7 = 12 (you subtract –7 from 5)
–8 + 3 = –5
–8 + –3 = –8 – 3 = –11
–8 – –3 = –8 + 3 = –5

Do you really find this difficult?
Adding is going to the right on the number line, subtracting towards the left

With + you will go towards the right on the number line.
Example: the red arrow. 0 + 6 = 6

With – you go towards the left on the number line.
Example: the blue arrow. 6 – 5 = 1

You can try to do the examples above with a number line.

4. Multiplying and dividing negative numbers

Remember this:
positive × positive = positive positive : positive = positive
positive × negative = negative positive : negative = negative
negative × positive = negative negative : positive = negative
negative × negative = positive negative : negative = positive
 
Examples
5 × 6 = 30
5 × –6 = –30
–5 × 6 = –30
–5 × –6 = 30
20 : 4 = 5
20 : –4 = –5
–20 : 4 = –5
–20 : –4 = 5


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