Fractions of Whole Numbers

Read this section to learn more about the history and notation of fractions, how to visualize them in relation to integers, and how to identify the different parts (numerator and denominator). Complete the practice questions and check your answers.

The Parts of a Fraction

A fraction has three parts.

  1. The fraction bar - .

    Fraction Bar
    The fraction bar serves as a grouping symbol. It separates a quantity into individual groups. These groups have names, as noted in 2 and 3 below.

  2. The nonzero number below the fraction bar.

    This number is called the denominator of the fraction, and it indicates the number of parts the whole quantity has been divided into. Notice that the denominator must be a nonzero whole number since the least number of parts any quantity can have is one.

  3. The number above the fraction bar.

    This number is called the numerator of the fraction, and it indicates how many of the specified parts are being considered. Notice that the numerator can be any whole number (including zero) since any number of the specified parts can be considered.

\frac{\text { whole number }}{\text { nonzero whole number }} \leftrightarrow \frac{\text { numerator }}{\text { denominator }}


Sample Set A

The diagrams in the following problems are illustrations of fractions.

Diagrams: 1a 1b 1c Figure 1. 

The fraction \frac{1}{3} is read as "one third..

2a. A whole rectangle

2b. The whole rectangle divided into 5 equal parts

2c. 3 of the 5 equal parts
Figure 2.

The fraction \frac{3}{5} "is read as "three fifths".

3a: The number line between 0 and 1

3b: The number line between 0 and 1 divided into 7 equal parts

3c: 6 of the 7 equal parts

The fraction \frac{6}{7} is read as "six sevenths."

4a. A whole circle

circle divided into 4 parts

4b: The whole circle divided into 4 equal parts

4c: 4 of the 4 equal parts
Figure 4. 

When the numerator and denominator are equal, the fraction represents the entire quantity, and its value is 1.

\frac{\text { nonzero whole number }}{\text { same nonzero whole number }}=1

Source: Rice University,
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