Fractions

fraction definitions
http://www.math.com/school/subject1/lessons/S1U4L1GL.html

Fraction refers to both a number and to the numeral.  When talking about the top number being the numerator and the bottom number is called the denominator we are thinking of the fraction as a numeral, and when we add two fractions we think of them as numbers.

3 <--- numerator
4 <--- denominator

3 Concepts

1. part-to-whole concept
This concept is the most common used for fractions.  It uses fractions to denote part of a whole.
Denominator:  Tells us how many equal parts are in the whole.
Numerator:  Tells us how many parts we are considering.
Teaching to kids
http://www.teach-kids-math-by-model-method.com/part-whole-concept.html
Example
The fractional part of an iceberg that is under water is 8/9.

2. Division concept
For any number a and b, with b not = to 0 a/b = a divided by b.
Sharing (partitive) concept:  dividing by 50 means there will be 50 parts
Example
dividing 25 pieces of gum to 50 people.  Each person will get 1/2 of a piece of gum.  There are 50 parts and each part is 1/2 of a whole piece of gum.
Video
http://www.youtube.com/watch?v=zq6on5kah3Q
Example
If you have 4 loaves of bread and you want to share it with 10 people you would cut the loaves into 10 equal pieces and each person would get 1/10.

3. Ratio concept
Fractions are used to compare one amount to another.
Example
A boys height is 1/3 of his mothers height.
Explanation
http://www.emathzone.com/tutorials/everyday-math/concept-of-ratio.html