**Rule 1** **Addition** of two Numbers with **the same sign** The result is the sum of the numbers with the given sign ( the sign of the two numbers ) .

## **Situation 1:** ++ =+

When **we add two plus numbers we get a plus number **

**Ex : 3+6=9. **

**Situation 2:** – – =+

When **we add two minus numbers we get a minus number but the value of the answer is more than the two additives that’s why its Plus sign
**

** Ex : -5 + – 6 = – 11** .

Example 5 + 6 + 8 = 19 . Example -5 + – 8 + – 6 = – 19 .

**Rule 2** : **Addition** of two numbers with **different signs ** the result is the difference **between the numbers** with the** sign of the” bigger number ” **.

**Situation 3: – + = –**

Ex 6 + – 9 = – 3 : Ex 19 + -5 = 14 . Ex -15 + 13 = – 2 .

In the above example the** answer is decreasing t**herefore negative sign applies.

Note Ex : 14 – 9 is the same as 14 + – 9 = 5 . and – 7 – 5 is really -7 + – 5 = – 12

Example simplify – 6 + 9 – 7 + 3 + 6 – 8 = – 6 – 7 – 8 + 9 + 3 + 6 = – 21 + 18 = – 3 .

Note we add the minus numbers ,we add the plus numbers then tidy it up .

**Rule 3 **: **Multiplication and signs **:

**The basic rules for multiplication and signs are as follows **

(**Minus ) x ( Minus ) = Plus . ( Minus ) x ( Plus ) = Minus , (Plus ) x (Plus ) = Plus** .

This can be expressed as follows that

(a) when we** multiply t**wo numbers with the** same sign ** we get **plu**s

( b) when we** multiply **two numbers with** difference signs ** we get a** minus **.

Example : – 7 x – 5 = + 35 , -7 x 5 = -35 . Example – 7. x – 4 x 3 = 28 x 3 = 84 .

**Brainstorming Questions: Can you tell why in the above conditions of rule 3 results are like that**

*Note: if we are asked to multiply three or more numbers remember you can only multiply two numbers at a time .*

*Example – 4 x -3 x 5 x -2 = 12 x 5 x – 2 = 60 . x – 2 = – 120 .*