3.1 Common Fractions as Division

A common fraction represents division of one number (the numerator) by another number (the denominator). For example, a number represented by the letter a divided by another number represented by the letter b, is written mathematically as:

The denominator of a common fraction designates the number of equal-sized parts into which some complete entity one whole is split or divided. The numerator of a fraction designates the number of parts being considered.

Examples of common fractions are:

Fractions are sometimes written using a slash (/) rather than a horizontal bar. This style should be avoided in technical work so that fractions are always seen in terms of division, hence and the order of operations is clear.

Technically, the fraction bar indicates a division operation wherein the numerator (top number) is divided by the denominator (bottom number). Although division is not actually performed every time a fraction is encountered, thinking of a fraction as a division problem is helpful when converting a common fraction to its decimal or percent form.

The fraction 2/3 indicates that 2 parts of an entity split into 3 equal parts is under consideration. For example, the first circle in Figure 3.1 is split into three equal sized pieces. In the second circle, 2 of the 3 pieces are shaded. We could say that the circle is 2/3 shaded. If the circle...