**Number **is a mathematical object used to measure, label and other mathematical operations. Basic mathematical operations are Addition, Subtraction, multiplication and division.

**Addition:**

The **addition** of two whole numbers is the total amount of those quantities combined.

Addition is written using the plus sign “+” between the terms; that is, in infix notation. The result is expressed with an equals sign. For example,

- (“one plus one equals two”)
- (“two plus two equals four”) and etc.,

**ADDITION SIGN RULES:**

**If signs are the same, add and keep the sign same:**

**Case 1:** If sign of both numbers are positive,then the result will have positive sign.

For example:

(a) (+3) + (+6) = (+9)

(b) (+18) + (+2) = (+20) and etc.,

**Case 2: **If signs o both numbers are negative,then the result will have negative sign.

For example:

(c) (-3) + (-6) = (-9)

(d) (-18) + (-2) = (-20) and etc.,

**If signs are different, then subtract and keep the sign of larger value.**

**Case 1: **If sign of the larger value us positive sign, then, the result will have positive sign.

For example:

(e) (+6) + (-3) = (+3)

(f) (-2) + (+18) = (+16)

**Case 2: **If sign of the larger value us negative sign, then, the result will have negative sign.

For example:

(e) (-6) + (+3) = (-3)

(f) (+2) + (-18) = (-16)

**SUBTRACTION:**

Subtraction is the operation of removing objects from a collection. It is written using the sign “-” between the terms. The result is expressed with an equals sign. For example,

- 2 – 1 = 1 (“two minus one equals 1”)
- 5 – 3 = 2 (“five minus three equals two”) and etc.

**SUBTRACTION SIGN RULES:**

**For example,**

Ex 2: (-10) – (+8)

= (-10) + (-8) = (-18) [Changed the sign from (+8) to (-8), then followed addition sign rule]

Ex 3: (-10) – (-8)

= (-10) + (+8) = ( -2) [Changed the sign from (-8) to (+8), then followed addition sign rule]

Ex 4: (+10) – (-8)

= (+10) + (+8) = (+18) [Changed the sign from (+8) to (-8), then followed addition sign rule]

Ex 5: (+10) – (+8)

= (+10) + (-8) = (+2) [Changed the sign from (+8) to (-8), then followed addition sign rule]

**Multiplication:**

The multiplication may be thought as a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the *multiplicand*, as the value of the other one, the *multiplier*.

“Normally, the multiplier is written first and multiplicand second.”

Multiplication is written using the sign “x” between the terms. The result is expressed with an equals sign. For example,

- 2 x 1 = 2
- 5 x 3 = 15 .

For example, 4 multiplied by 3 (often written as 3 x 4 and said as “3 times 4”) can be calculated by adding 3 copies of 4 together:

3 x 4 = 4 + 4 + 4 = 12

MULTIPLICATION SIGN RULE:

**IF THE SIGNS ARE SAME, MULTIPLY AND PUT POSITIVE SIGN.**

Case 1: If the signs are positive then multiply and put positive sign.

For example:

(a) (+3) x (+6) = (+18)

(b) (+10) x (+2) = (+20)

Case 2: If the signs are negative then multiply and put positive sign.

For example:

(a) (-3) x (-6) = (+18)

(b) (-10) x (-2) = (+20)

**IF THE SIGNS ARE DIFFERENT, MULTIPLY AND PUT NEGATIVE SIGN IRRESPECTIVE OF VALUE OF THE NUMBER.**

For example:

(a) (+3) x (-6) = (-18)

(b) (-3) x (+6) = (-18)

**DIVISON:**

**Division** is the opposite of multiplying. It is written using the sign “÷ or /” between the terms. The result is expressed with an equals sign.

When we know a multiplication fact we can find a**division** fact:

**DIVISION SIGN RULE: **

**DIVISION SIGN RULE IS SAME AS MULTIPLICATION, SO FOLLOW MULTIPLICATION SIGN RULES.**

For example:

^{(a) (-15)}/_{3} = (-5) [Multiplication sign rule: if signs are different then put negative sign]

^{(b) (15)}/_{(-3)} = (-5) [Multiplication sign rule: if signs are different then put negative sign]

^{(c) (-15)}/_{(-3)} = (+5) [Multiplication sign rule: if signs are same then put positive sign]

^{(d) (+15)}/_{(+3)} = (+5) [Multiplication sign rule: if signs are same then put positive sign]

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