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# Sign Rules

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

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, $1 + 1 = 2$ (“one plus one equals two”) $2 + 2 = 4$ (“two plus two equals four”) and etc.,  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 adivision 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]