Here are some lessons that provide a basic understanding of fractions.
MATH MILESTONE #B4: PROPERTIES OF FRACTIONS
To summarize:
When the division is not exact, a remainder is left after division. The remainder is less than the divisor, and it may be looked upon as a portion of the divisor. Such portions are called fractions. A proper fraction, such as “half,” is always less than one.
In the absence of a proper notation for a quantity less than 1, a fraction is presented as a “dividend over divisor.” These two numbers are called numerator and denominator respectively to emphasize the fact that a fraction is a single quantity even when two numbers are used to represent it.
When a unit is divided into equal number of smaller parts, each part is called a unit fraction. The larger is the number of parts the smaller is each part or unit fraction. The numerator of a unit fraction is always 1. All other fractions are multiples of unit fractions.
In a proper fraction the numerator is less than the denominator making it less than 1. In an improper fraction, the numerator is equal to, or greater than the denominator making it equal to, or greater than 1. Improper fractions may be written as mixed numbers.
Equivalent fractions are those which are written with different numerator/denominator pair, but represent the same portion of a unit. For example, both 1/2 and 2/4 represent “half” of a unit. In such a case, the numerator/denominator pair of a fraction is “magnified” or “shrunk” by the same amount to become the numerator/denominator pair of the equivalent fraction.
Like fractions are multiples of the same unit fraction. Unlike fractions are multiples of different unit fractions. Like fractions may be compared simply by their numerators. To compare unlike fractions, one must convert them to like fractions first.
Here are some related videos from the Khan Academy.
Mixed numbers and improper fractions
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