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Secondary 1 Math: The 4 Golden Rules of Negative Numbers

by Jimmy Ling


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


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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