Fractions

fractions as division (equal sharing)

Guiding Question: How can equal sharing contribute meaning to fractions?

Fractions as Quotients: A fraction represents the result of division.
The Parts:
- - Numerator: The top number; the quantity being shared.
  - Denominator: The bottom number; the number of shares.
Conversion: You can convert a fraction to a decimal by dividing the numerator (top number) by the denominator (bottom number).

Guiding Question: How can the addition and subtraction of fractions be generalized?

Common Denominators: You can only add or subtract fractions if they have the same "unit" (denominator).
Related Denominators: If one denominator is a multiple of another, multiply the smaller one to match.
The Procedure: Multiply the numerator and denominator by the same factor to find the common denominator, then, add/subtract the numerator.

Guiding Question: How can an understanding of multiplication be extended to fractions?

Interpretation: Multiplying by a fraction is like taking a "part" of a whole; the result can be smaller than the original number.
The Procedure: Multiply the natural number by the numerator, then divide by the denominator.
Unit Fractions: Multiplying by a unit fraction (like 1/4) is the same as dividing by its denominator.

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