Objectives

After reviewing this unit, you will be able to:

• Identify the components of a fraction.
  
• Compare and order fractions with like denominators.
  
• Compare and order fractions with like numerators.
  

Components of a Fraction

A fraction is a number that is written in the form:

or a/b

• The a is the numerator, and the b is the denominator.
  
• The line separating the numerator and denominator is a fraction bar.
  

Fractions are used when representing numbers that describe the parts of a whole. The fraction a/b also can be read as "a out of b," "a over b," or "a divided by b."

There are some restrictions on a and b.

• Both a and b must be integers, meaning positive and negative whole numbers.
  
• The denominator, or b, cannot be zero. This is because one cannot divide by zero.
  

Often you will read information that could be represented as a fraction. Below is an example of this type of information.

Example

If there are 18 students in a classroom, and 6 of the students wear glasses, what fraction of the students wear glasses?

A fraction can be thought of as "a out of b." In the following picture Total number of students is 18. Number of students with glasses is 6. Number of students with glasses out of the whole class is 6/18.

Comparing Fractions with Like Denominators or Like Numerators

Comparing fractions gives you a sense of how items relate. Now let's take a look at some fractions and see how changing the numerator, and then the denominator, changes a fraction.

Example

In each of the diagrams below, the shaded part represents the fraction shown at the left of each rectangle.

The first rectangle has 1/1, or the whole rectangle shaded. As you move down:

The numerator (top) of each fraction remains the same, the integer 1. The denominator (bottom) increases. As the denominator gets larger, the shaded fraction gets smaller.

The first rectangle has 1/8 shaded. Then, as you go down:

The numerator (top) of each fraction increases. The denominator (bottom) remains the same, the integer 8. As the numerator gets larger, the shaded fraction gets larger.

We can draw the following conclusions:

• When the numerator stays the same, and the denominator increases, the value of the fraction decreases.
  
• When the denominator stays the same, and the numerator increases, the value of the fraction increases.
  

You have now completed this unit. Try the practice problem below before moving on.

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