Adding Integers - Algebra

ADDING TWO \ALIKE SIGNS – two positive numbers or two negative numbers


First Method:


1. Add absolute values


2. Attach same sign to the answer


Example:

Adding two positives integers

4 + 5 = 9



Adding two negative integers

(-4) + (-5) =


(-9)


Second Method:


(+) positive (-) negative

Draw (+) and (-) to represent the number sentence.


Note: A pair of (+) and (-) cancels each other or equals zero. (See end of page for more an illustration.)


4 + 5 = 9

+ + + + and + + + + +



OR

(-4) + (-5) = (-9)


(-) (-) (-) (-) and

(-) (-) (-) (-) (-)

Parentheses are used for clarity only.

Are there any zero pairs to cancel? No. So, count the signs to get a total.


Memory tip for adding two integers with same signs:Alike Signs –Add




ADDING TWO UNLIKE SIGNS

- 6 + 4 = ?

First Method:

1. Subtract absolute values

2. Use the sign of the number with the larger absolute value

| - 6| = 6 | 4 | = 4



Remember to put the larger number first when subtracting two numbers. -- > 6 - 4 = 2

Six is larger. So, the answer will have a negative sign.

- 6 + 4 = - 2


Second Method:

Parentheses are used for clarity only.


(-) (-) (-) (-) (-) (-)

+ + + +

Are there any zero pairs to cancel? Yes. Four pairs cancel each other. So, count the remaining signs to get a total. Two negatives are left. Thus, - 6 + 4 = - 2


Memory tip for adding two integers with unlike signs:Different Signs – Find the Difference



Here is proof that a positive and negative cancel each other.

( -3) + 3 = ?


(-) (-) (-)

+


+ +

Three negative / positive pairs cancel each other. Thus, the answer is zero.




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