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.
A fraction has three parts.
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.
Denominator
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.
Numerator
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.
The diagrams in the following problems are illustrations of fractions.
Diagrams: | 1a. | 1b. | 1c. | Figure 1. |
2a. A whole rectangle |
2b. The whole rectangle divided into 5 equal parts |
2c. 3 of the 5 equal parts |
Figure 2. |
The fraction "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 is read as "six sevenths."
4a. A whole circle |
4b: The whole circle divided into 4 equal parts |
4c: 4 of the 4 equal parts |
Figure 4. |
Source: Rice University, https://cnx.org/contents/XeVIW7Iw@4.6:Bh4M3l5x@2/Fractions-of-Whole-Numbers
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