## Multiplying Positive and Negatives numbers

We can only do arithmetic in the usual way.

To calculate 5(−2), we have to do 5· 2 = 10 — and then decide on the sign.

Is it +10 or −10?

For the answer, we have the following Rule of Signs.

## Rules of signs

Like signs produce a positive number;

unlike signs, a negative number..

if the value of x is positive, then the value of −x must be negative, and vice-versa.

Since we call the positive or negative value of a number its sign, then we can state the following principle:

A minus sign changes the sign of a number.

On the number line, a minus sign reflects a number symmetrically about 0. You can observe it in the following picture:

When you multiply:

**+ times +** two positives make a positive:**+ **3∙2=6

**– times – **two negatives make a positive:** + **(-3)∙(-2)=6

**– times +** a negative and a positive make anegative: **–** (-3)∙(2)=-6

**+ times –** a positive and a negative make a negative: **–** 3∙(-2)=-6

### Formal rule:

A formal rule is simply a rule we write with letters. We write it with letters because we want it to apply to any numbers:

**Rule for 0:**

Any number, multiplied by 0, gives 0 as a result.

a·0=0

## Dividing Positive and negative numbers

**Reciprocal**: two numbers are reciprocals if their product is 1:

A division is a multiplication by the reciprocal:

When you divide, the rule is the same as for multiplication!

**+ divided by +** two positives make a positive: **+ **6÷2=3

**– divided by- **two negatives make a positive:** + **(-6)÷(-2)=3

**– divided by+** a negative and a positive make a negative: **–** (-6)÷(2)=-3

**+ divided by-** a positive and a negative make a negative: **–** 6÷(-2)=-3