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What are the rules for multiplying and dividing negative or minus numbers.

Updated on February 20, 2013


Multiplying negative numbers is actually quite a simple process providing that you remember these 2 rules:

Rule A: If the two numbers that are being multiplied have different signs then the answer will be a negative number.

Rule B: If the two numbers that are being multiplied have the same signs then the answer will be positive.

Example 1

Work out the answer to -6 × -3.

First, forget about the negative numbers and multiply the two numbers together:

6 × 3 = 18.

Now since -6 and -3 have the same signs (both negative) then the answer will be a positive number.

Therefore:

-6 × -3 = +18 (or just 18 as the positive sign is not really needed)

Example 2

Work out the answer to -7 × +8.

First, forget about the negative numbers and multiply the two numbers together:

7 × 8 = 56.

Now since -7 and +8 have different signs (one negative and the other positive) then the answer will be a negative number.

Therefore:

-7 × +8 = -56

Example 3

Work out the answer to +9 × -6.

First, forget about the negative numbers and multiply the two numbers together:

9 × 6 = 54.

Now since +9 and -6 have different signs (one positive and the other negative) then the answer will be a negative number.

Therefore:

+9 × -6 = -54

One word of warning should be made - make sure you only apply these rules to 2 numbers at a time. If you have 3 numbers that are multiplied together multiply the first 2 numbers together, and then multiply this answer by the last number.

Example 4

Work out 3 × -7 × -4.

First work out 3 × -7 which is -21 (the answer is negative as the signs are different).

Next work out -21 × -4 which is 84 (the answer is positive as the signs are the same).

So 3 × -7 × -4 = 84

Example 5

Work out -2 × -8 × -3

First work out -2 × -8 which is 16 (the answer is positive as the signs are the same).

Next work out 16 × -3 which is -48 (the answer is negative as the signs are different).

So 2 × -8 × -3 = -48

So just remember same signs give a positive answer and different signs give a negative answer. Also these same rules can be applied to division, however, don’t apply these rules to adding and taking numbers as you will go wrong (the best approach to adding and taking is to use a number line).

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