Working with Signed Number

Working with Signed Number
 
While solving problems in algebra there are times when you have to add, subtract, multiply or divide a signed number. That really comes in hardy, but if you follow these rules below or you use a number line, it`s simple as ABC.

Adding numbers with sign
You can add positive number to positive number, negative number to negative number, or  negative number to positive number and vice versa.
To add positive number to positive number and negative number to negative number keep in mind that , when the sign are the same you will find the sum (adding the first with the second), and the sign in-front of the two number is the sign of the sum (answer).

(+a) + (+b) = +ab                       (-a) + (-b)=  -ab
Examples:
    1. (+4) + (+9) = +13 positive against positive
    2. (-10) + (-6) = -16 negative agaist neagtive

and there are times where you have to a long tail addition
    3. (+4) + (+6) + (+10) + (+3) = +23
    4. (-7) + (-3) + (-5) + (-2) = -17.

While adding numbers with different sign, first find thier different, and the sign of the diferent (answer) is the sign of the number father from zero.
Examples:
    1.(+9) + (-6) = +3
    2. (-6) + (+9) = +3.

Note: I first find the differencs between 9 and 6 which is 3 (in both examples above) and then find the number farther from 0 which is 9 (count like this 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...) so the sign of the difference will be +, because it`s the sign of 9 (number farther from 0).
    3. (-3) + (+8) = +5
    4.(+2) + (-5) = -3.

Also note that  8 and 5 are farther rom zero.
Subtracting numbers with sign
To sutract a signed number,what we need is just to change the minus sign to plus and change the sign of the number at the right of the minus to it`s opposite sign.
(+a) - (+b) = (+a) + (-b)
(+a) - (-b) = (+a) + (+b)
(-a) - (+b) = (-a) + (-b)
(-a) - (-b) = (-a) + (+b).

After you change the signs as explain above, then following the adding number with sign you could solve the question very easy.
Examples:
    1. (+3) - (+4) = (+3) + (-4) = -1
    2.(+6) - (-2) = (+6) + (+2) = 8
    3. (-7) - (+5) = (-7) + (-5) = -12
    4. (-5) - (-3) = (-5) + (+3) = -2.

In the example 1 above the subtraction becomes addition and the sign infront of 4 is also change, because we are adding number with different sign, we first find the different and insert the sign of the number farther from 0. All the examples follow the same rule and do the addition after changing the signs (as explained).
Multipling and Dividing numbers with sign
Multipling or dividing number with sign are really easy provided the rule are followed, it realy a simple rule. when multipling or dividing numbers with the same sign, the answer sign result in positive; also when the signs are different, it result in negative.
(+a) × (+b) = +ab
(+a) ÷ (+b) = +(a/b)
(+a) × (-b) = -ab
(+a) ÷ (-b) = -(a/b)
(-a) × (+b) = -ab
(-a) ÷ (+b) = -(a/b)
(-a) × (-b) = +ab
(-a) ÷ (-b) = +(a/b)
Examples:
    1.(+5) × (+4) = +20
    2. (+3) ÷ (+3) = +1
    3. (+9) × (-2) = -18
    4. (+8) ÷ (-2) = -4
    5. (-4) × (+2) = -8
    6. (-12) ÷ (+4) = -3
    7. (-5) × (-8) = +40
    8. (-14) ÷ (-7) = +2
Notice that in each example above it doesn`t matter which comes first, either the addition sign or the subtraction sign in both the multiplication and division. There may be situation whereby you will have to do such multiplication or division but in three or four value, here is how.
Count the number of the negative, if it result in even it means the answer`s sign is positive but if it result in odd the  sign of the result is negative.
Examples:
    1. (+5) * (-3) * (+7) = -105
    2. (+2) * (-5) * (+4) * (-3) = +120
    3. (-12) / (-2) * (+3) = +18
    4. (+2) * (-8) / (-2) * (-3) = -24
It good you make it to the end, make sure you give some test and share then with me, or if you need to ask something comment below.