Marlene's How To Work With Fractions Basics   
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Basics

Fractions A fraction is the division of two numbers. Fractions are used to express portions smaller than a whole and to divide multiple objects into groups.

In a fraction, the number above the "/" is called the numerator.
The number below the "/" is called the denominator.


For example in the fraction   3/4
  • The "3" is the numerator
  • The "4" is the denominator
Notes:
  • A denominator of zero (like 6/0) is undefined.
  • To convert a whole number into a fraction, just make the whole number the numerator and the denominator a 1

    Example:  10 is equal to 10/1

Examples of Fractions:  1/2, 2/2, 4/3
Proper Fractions A Proper Fraction is a fraction where the denominator (the bottom number) is greater than the numerator (the top number).

Examples of Proper Fractions:  3/4, 1/9, 125/213
Improper Fractions An Improper Fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).

Note:
To Convert a Whole Number to a Fraction, simply place the Whole Number over "1"
Example: 10 converts to 10/1

Examples of Improper Fractions:  4/3, 19/7, 6/6, 30/1
Mixed Numbers A Mixed Number is an expression which consists of a whole number and a proper fraction (a fraction where the numerator is less than the denominator).   

Note:
To Add, Subtract, Multiply, or Divide a Mixed Number, first convert the Mixed Number to an Improper Fraction.

Examples of Mixed Numbers:  1 1/2,   2 5/7,  3 7/8
Prime Numbers A Prime Number is a number which can only be divided by 1 and itself.

Prime Numbers are used in Factoring fractions

Prime Numbers (up to 100):
       2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
       61, 67, 71, 73, 79, 83, 89, 97


Some Hints for finding prime numbers:
  • A number is divisible by 2 if its an even number (the "ones" digit of the number is a 0, 2, 4, 6, or 8).
  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 5 if its last digit is 0 or 5.


0 and 1 are the only numbers that are neither composite nor prime.
Composite Numbers A Composite Number is a number that has more than two factors other than 1 and itself.
All Composite Numbers can be factored into prime numbers.

The first 105 composite numbers are:
       4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28,
       30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51,
       52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74,
       75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94,
       95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114,
       115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128,
       129, 130, 132, 133, 134, 135, 136, 138, 140

Examples:
  • The number 14 is a composite number because it can be factored as 2 * 7
  • The numbers 2 and 3 are not composite numbers because each of them can only be divided by one and itself


0 and 1 are the only numbers that are neither composite nor prime.
Factoring Factoring is used to simplify (reduce) a fraction to its lowest terms.

A fraction is simplified when its numerator and denominator have no common factors (ie, the fraction is reduced or in lowest terms).

One method to find the prime factors of a number is to divide the number by the Prime Number in order, starting with 2, and working up until the quotient is a Prime Number.

Example: Find the prime factors of 1638
  • 2 - Since 1638 is even, it is divisible by 2: 1638/2 = 819

  • 3 - Since the result from the last step, 819, cannot be divided by 2 again, try
         dividing it by 3 (the next prime number): 819/3 = 273

  • 3 - Try dividing the result from the last step, 273, by 3 again: 273/3 = 91

  • 7 - Since the result from the last step, 91, cannot be divided by 3 again-- try
         dividing by 5 (the next prime number).
         Since 91 is NOT divisible by 5, try 7 (the next prime number):
         91/7 = 13

  • 13 - Since the result from the last step, 13, is a prime number,
           factorization is complete.

  • Answer:
    The prime factors of 1638 are:    2, 3, 3, 7, 13
    Since 2 * 3 * 3 * 7 * 13  =  1638.