Mathematics Chapter 1.2 and 1.3 Addition and Subtraction of Real Numbers

For example when adding two numbers that are opposites, such as 2 and -2, the sum is 0. We call such numvers

Additive inverses. Every real number has an opposite, or additive inverse.

To subtract real number

Change the operation of subtraction to addition and change the number being subtracted to its opposite. Follow the rule for adding real numbers.

Additive identity property

For any real number a, a+0=a and 0+a=a. In words, this property states that any number added to 0 is the original number.

Associative Property of Addition

For any three real numbers, a,b, and c. (a+b)+c=a+(b+c). The associative property of adding lets us regroup numbers that are added without affecting the sum.

Commutative property of addition

For any two real numbers a and b, a+b=b+a. The commutative property of addition allows us to add numbers in any order, getting the same sum.

To add real numbers

If the number have the same sign, add their absolute values and keep their sign. If the numbers have different sign, find the difference between the larger absolute value and the smaller absolute value, and take the sign of the number with the latter absolute value.

When using the number line to add two real numvers, move to the left if the second number is

Negstive and to the right if it is positive.

For any real number a, there is exactly one real number -a such that

a+(-a)=0 and (-a)+a=0. In words this property states that any real number added to its opposite is zero.