| 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.
Examples of Fractions: 1/2, 2/2, 4/3 |
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| Proper Fractions |
A Proper Fraction is a fraction where the denominator is greater than the numerator.
Examples of Proper Fractions: 3/4, 1/9, 125/213 |
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| Improper Fractions |
An Improper Fraction is a fraction where the numerator is greater than or equal to the denominator.
Examples of Improper Fractions: 4/3, 19/7, 6/6, 30/1
Note:
To Convert a Whole Number to a Fraction, simply place the Whole Number over "1"
Example: 10 converts to 10/1
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| 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).
Examples of Mixed Numbers: 1 1/2, 2 5/7, 3 7/8
Note:
To Add, Subtract, Multiply, or Divide a Mixed Number, first convert the Mixed Number to an Improper Fraction.
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| 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.
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| Composite Numbers |
A Composite Number is a number that has more than two factors of 1 and itself. All composite numbers can be factored into prime numbers.
0 and 1 are the only numbers that are neither composite nor prime.
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| 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, 819, cannot be divided by 2 again, try
dividing it by 3 (the next prime number): 819/3 = 273
- 3 - Try dividing the result, 273, by 3 again: 273/3 = 91
- 7 - Since the result, 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, 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.
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