Adding and Subtracting Real Numbers Sections 4 & 5

The Identity Property of Addition states that any number plus 0 will equal itself. x+0=x

Example: 3+0=?

The Inverse Property of Addition states that any number plus its own negative counterpart equals 0. y+(-y)=0

Example: 3+(-3)=?

You can use a number line to add or subtract by starting on the first number, and counting right (for addition), and left (for subtraction).  The second number in the equation is the amount of spaces you will count to the left or right.

example:    x1 >                       x2

              |---|---|---|---|---|---|---|---|---|---|     -4+6=2                 Key: x1= first number

            -5  -4  -3  -2  -1   0   1   2  3   4   5                                          x2= answer

                                                                                                         </>= direction of counting

                   x2                            < x1

example:|---|---|---|---|---|---|---|---|---|---|      3-7=?

            -5  -4  -3  -2  -1   0   1   2  3   4   5

When you add 2 numbers with the same sign, just add them like normal, and keep the sign.

When you add 2 numbers with different signs, just subtract the smaller number from the bigger number and keep the bigger number's sign.

Example -3+(-4)=-7    -8+5=(-3)    -7+4=?

               3+4=7          8+(-5)=3     -3+-86=?

A matrix is a grid pattern of numbers.  The numbers inside the brackets are the elements.  The lines of numbers going across are rows, the lines of numbers going up and down are columns.  You can only add or subtract matrices with the same dimensions, or number of columns and rows.

Example:[-3  2 5]   +  [ 2   2 -4]  =[-1 4  1]   

               [ 4 -5 2]  +  [-5 -4   6]  =[-1 -9 8]

To subtract a number, add its opposite.

Example: 6-7=(-1) is the same as 6+(-7)=(-1)

The Absolute Value of a number is its distance from 0 on a number line.  Basically,the absolute value of any number that is in between the lines is the same as the original number except made positive if it was negative, and it just stays the same if it was already positive.  Both -3 and 3 are 3 units from 0.  You write "the absolute value of -3" as |-3| (the answer would be  |-3|=3.)

Example: |3+8|=11   |-3+8|=5   |3+-8|=5   |-3+-8|=11

                       |-4+6|=?

Evaluating expressions is when you will get a prblem with letters in it, and above the problem, it will say what number the letters equal.  You just substitute the corresponding number in place of the letters, and solve the problem.

Example: x=2  y=-3 z=4

                (3y)+zx=(-1) is the same as (3*-3)+4*2=(-1)

                1z-3z=?        yy=?          (yx)/(3yz)=?