POSITIVE AND NEGATIVE NUMBERS

POSITIVE AND NEGATIVE NUMBERS

When no sign precedes a term,the sign + is always understood.

The use of the signs + and - is so constant and so important .The magnitude of a quantity considered apart from its sign is called its absolute magnitude.Thus a gain of Rs 5 and a loss of Rs 5 ,are equal in magnitude though opposite in sign.

Addition: If two positive numbers are added together the sum is positive and if two negative numbers are added together the sum is negative ,but if a positive number and a negative number are added together the result will be positive or negative according as the positive or negative number has greater numerical absolute value.

+4+ (+3)=+7

+7+ (-4)=+3

5+ (-8)= -3

(-3) + (-4) = -7

In adding up numbers it is immaterial in what order we take them,provided that each number has its own sign placed before it.

Subtraction:

To subtract a positive number means to add the corresponding negative number and if the number to be subtracted is negative,change it into a positive number, and then add the number so changed to the number from which it was originally to be subtracted.

+ 8 - ( +3) = +5

3- (+8) = -5

+5-(-3)= 8

-8- (-3) = -5.

Multiplication:

the meaning of 5 x 3 is that we have to take 5 three times.Hence multiplication is repeated addition.The number multiplied is the multiplicand and the number that multiplies is the multiplier,while the result is the product.

+ 5 x ( + 3 ) = + 15

- 5 x ( +3 ) = -15 

+ 5 x (-3) = -15

-5 x -3 = +15.

The product of two positive or two negative numbers is positive while the product of two numbers opposite in sign is negative.

In other words , in multiplication two like signs give + and two unlike sign give -.This is known as the sign law of multiplication.

Division:

Division is the inverse operation of multiplication.

dividend = divisor x quotient + remainder

(+ab) ➗( + b) =+a

(-ab )➗ ( + b)= -a

( + ab ) ➗ ( -b) = -a

( -ab ) ➗ ( -b )= + a

When both dividend and divisor have like signs , the quotient is positive ,and when they have unlike signs , the quotient is negative.

In short like signs give + , and unlike signs give - Thus the law of signs for division is the same as that for multiplication.

Any power of a positive number is positive and an even power of anegative number is positive but an odd power of a negative number is negative.

every positive number has two square roots both equal in magnitude but opposite in signs.

√x2 = x or -x