# Secondary 1 Math: The 4 Golden Rules of Negative Numbers

In my previous post for secondary 1, I have went through “Number Line and Negative Numbers“. You have learnt how to do addition and subtraction which involve negative numbers.

Now, I want to share on how to do **multiplication and division** which involve negative numbers.

You need to memorise the 4 golden rules.

## Rule 1: Positive x Positive = Positive

I am sure you are very clear on this. When you take a positive number multiply by a positive number, the answer is positive.

Example: 2 x 3 = 6

Note that 2 and 3 are positive numbers. The answer is 6 which is positive too.

## Rule 2: Negative x Positive = Negative

When you take a negative number multiply by a positive number, the answer is negative.

Example: -2 x 3 = -6

You can think of it this way. You don’t have any marble. You need to give 3 people 2 marbles each. So the total shortage is 6 marbles. You can treat the negative sign as a shortage.

## Rule 3: Positive x Negative = Negative

This is similar to rule 2. When you take a positive number multiply by a negative number, the answer is negative.

Example: 2 x -3 = -6

## Rule 4: Negative x Negative = Positive

Now things start to get a bit interesting. When you take a negative number multiply by a negative number, the negative sign will cancel away and the result will be positive.

Example: -2 x -3 = 6

Why does 2 negatives give us a positive?

You can think of it this way. Treat positive as “Do” and negative as “Do not.”

If I put 2 negatives together and say “Do not do not study,” what am I trying to say?

The answer is “Study!”

The “do not” and “do not” will cancel away and the final result is “Study”.

The same logic applies for multiplication and division.

## The Same Set of Rules apply for Division

Examples:

6 ÷ 2 =3

-6 ÷ 2 = -3

6 ÷ -2 = -3

-6 ÷ -2 = 3

## How to Memorise the 4 rules

There is a shortcut. If you multiply 2 numbers of the **same sign** (for instance positive and positive or negative and negative), the final result will be positive.

But if you multiply 2 numbers of the **opposite sign** (for instance positive and negative or negative and positive), the final result will be negative.

## Some other Tips:

When a number has no sign, it means it is positive. Example “5 = +5”

Sometimes we put brackets around a number to avoid confusion.

Examples: 2 x (-3) = -6

(-2) x (-3) = 6

-(-2) is the same as minus times minus 2 which is equal to 2.

## Extending the Same Rules to Algebra

The same rules apply for Algebra as well!

2a x 3 = 6a

-2a x 3 = -6a

2a x -3 = -6a

-2a x -3 = 6a

Do memorise and know how to apply these 4 rules because you will be using them many times in secondary 1 math and later years.

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