Math Tutor Bob

bob@mathtutorbob.com

Helping you succeed in math.

Prequisites for Algebra


Algebra is a difficult enough subject. Don't make it worse by not knowing what you should know when the class starts. The most important prerequisite is to learn the math facts.

Multiplication
Division
Adding and Subtracting Numbers


Also, the "fact monster"
is a great site on the internet to practice the math facts.

If you need your fingers to multiply, add or subtract then you do NOT adequately know your math facts. You should feel very comfortable with the following subjects/concepts:

Addition of integers

       8+5       17+48  1456+3201       5401+10223
       121+2232  88+44  329123+9908887
If any of the above give you a problem you need to spend time understanding how to do these problems. Help

Subtracting integers

       8-5       217-48   3456-3201     15401-10223
       3121-2232 88-44    329123-99887

If any of the above give you a problem you need to spend time understanding how to do these problems.

Adding/subtracting negative numbers

       -7+6   9-12+4   90-100+2     -11-30-4   -34-48-2+200
       6-2   -2+6      -3-5-12+30   -44-12-3
If any of the above give you a problem you need to spend time understanding how to do these problems. The number line is always a good tool in solving addition and subtraction problems.

Handling signs in addition/substraction and mult/div

       -4-(-4)      5+(-10)        -8-(-10)      -100-(-200)
       -4-8-(-7)    -12-30+(-20)   -(-30)+32
If any of the above give you a problem you need to spend time understanding how to do these problems.

Dividing integers

       9/3      36/9    45/5   54/6   18/2   42/6   63/7
       81/9     40/10   56/8   42/7   27/3   32/4   22/22
If any of the above give you a problem you need to spend time understanding how to do these problems, which is just basically memorizing the division facts.

To recap what multiplication and division are though, lets look at multiplication.

  Consider 6 + 6 + 6 + 6 that is 6 added 4 times or 4 sixes. 
    And multiplication is just a shortcut for doing such 
    addition.

  6 + 6 + 6 + 6 is the same as 4 times 6 or 4 * 6 or 4(6) 
    which are different ways to indicate multiplication.

  And division is the opposite of multiplication. 
    The problem 24 / 6

  24 divided by 6 can also be expressed as how many times 
       can six be subtracted from 24.
  24 / 6 is, of course, equal to 4. And 6 can be subtracted 
       from 24 four times, as illustrated below.

        24 - 6 = 18  1 time
        18 - 6 = 12  2 times
        12 - 6 = 6   3 times
         6 - 6 = 0   4 times 
		 
    Also, note that there is zero (0) remaining.
		 
Sometimes in division there is a remainder. Consider 26 / 4 which is 6 with a remainder of two. Or
        26 - 4 = 22  1 time
        22 - 4 = 18  2 times
        18 - 4 = 14  3 times
        14 - 4 = 10  4 times
        10 - 4 = 6   5 times
         6 - 4 = 2   6 times and we cannot subtract 4 
                       any more, but there is 2 left 
                       over as a remainder.

Multiplying by 10, 100, 1000, etc

     When multiplying by 10, 100, 1000, etc .... 
     just count the zeros and move the decimal 
     point that many places to the right in the 
     other number. That is to say:

34 * 100 Count the zeros = 2 Move decimal in 34 (which is 34. ) to the right twice 3400 Answer
1047 * 10000 Count zeros = 4 Move decimal 4 times to the right 10470000 Answer
This rule also works for decimal numbers. Say, 45.38 * 10 Count zeros = 1 Move decimal one time to the right 453.8 Answer

Dividing by 10, 100, 1000

Dividing by 10, 100, 1000, etc is very similar multiplying with one little difference. When dividing by 10, 100, 1000, etc .... just count the zeros and move the decimal point that many places to the left in the other number. That is to say:
  3496 / 100
    Count the zeros = 2
    Move decimal in 3496 (which is 3496. ) to the left twice
       34.96 Answer

    104768 / 10000
      Count zeros = 4
      Move decimal 4 times to the left
         10.4789 Answer

                
  This rule also works for decimal numbers. Say,

    45.38 / 10
       Count zeros = 1
       Move decimal one time to the left
                       (since it is division)
           4.538 Answer