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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Directed Numbers


Numbers can either be positive or negative. The name directed number comes from thinking of a number line. The directed part saying which direction from 0 on the number line the number lies: positive numbers being one direction and negative being the other.

Sometimes brackets are put around negative numbers to make them easier to read, e.g. (-2). Other times a '+' or '-' sign is written in front of the number. Both methods are used and you need to be happy using both. If a number is positive, the + is usually missed out before the number. So 3 is really (+3) or +3.


Adding and multiplying combinations of positive and negative numbers can cause confusion and so care must be taken.

Addition and Subtraction

When adding and subtracting directed numbers there are a couple of rules you can use to help you work out the answer:

  • Two 'pluses' make a plus - so if two '+' signs are written next to each other you can replace them with a single '+' sign.
    • Thus -3 + (+2) = -3 + 2 = -1
  • Two 'minuses' make a plus - so if two '-' signs are written next to each other, you can replace them with a single '+' sign.
    • Thus 6 - (-2) = 6 + 2 = 8
  • A plus and a minus make a minus - so if one of each sign sit next to each other, then you can replace them with just a '-' sign.
    • Thus -4 - (+3) = -4 - 3 = -7 and 3 + (-7) = 3 - 7 = -4

Basically when adding and subtracting directed numbers different signs next to each other mean subtract, the same signs next to each other means add.

Multiplication and Division

Here there are again three simple rules to follow:

  • If two positive numbers are multiplied together or divided, the answer is positive.
    • Thus 2 x 4 = 8 and 10 ÷ 2 = 5
  • If two negative numbers are multiplied together or divided, the answer is positive.
    • Thus (-2) x (-4) = 8 and (-10) ÷ (-2) = 5
  • If a positive and a negative number are multiplied or divided, the answer is negative.
    • Thus (-2) x 4 = (-8) and 10 ÷ (-2) = (-5)

So basically, when multiplying or dividing two numbers, if your numbers have the same sign the answer is positive, but if the two numbers have different signs the answer is negative.

i think its all right took me awhile to find it though

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