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Fractions: Bits and Pieces

Fractions are used often, for instance when adding leftover pails of foam or mixing gas and oil for chain saw fuel. Fractions allow the use of parts of a number or combinations of parts and whole numbers, such as half, two and a half, or two eights. The remainder found in long division can be changed to a fraction. Like whole numbers, fractions can be added, subtracted, divided, and multiplied. Fractions can also be represented as decimals (see Section 1.6).

A fraction consists of a numerator (top number) and a denominator (bottom number).

The numerator represents the number of parts available.

The denominator represents the number of parts in a whole.

Example 1 - What fraction of the box in the figure below is shaded? What fraction is not shaded?



The box is divided into five parts. Two of those five parts are shaded. The shaded fraction represents two fifths. In this case, two fifths of the figure is shaded.

Three of the five parts are not shaded. The unshaded fraction represents three fifths. In this case, three fifths of the figure is not shaded.

Whole Numbers as Fractions

Fractions can also describe whole numbers or a whole number with a remainder expressed as a fraction. For example, a whole number can be written as:

four over two, eight over four, or thirty-two over sixteen


The whole number 1 can be written as:

one over one, three over three, seven over seven, etc.


Fractions larger than 1 have a larger number in the numerator or top part of the fraction.

four thirds, eight fifths, and three seconds are all larger than 1.