Defining Fractions Study Guide

Updated on Aug 24, 2011

Find practice problems and solutions for these concepts at Defining Fractions Practice Problems.

What's Around The Bend

  • Defining a Fraction
  • Parts of a Fraction
  • Writing Fractions
  • Using Fractions to Represent Real Situations
  • Proper and Improper Fractions
  • Like and Unlike Fractions
  • Comparing Fractions
  • Equivalent Fractions
  • Simplifying Fractions

Defining a Fraction

What is a fraction, and why do we need them? A fraction is a type of number. We use fractions to represent a part of a whole. Let's say a whole pie is made up of eight slices. If you eat two slices, what part of the whole pie have you eaten? Fractions help us answer that question. You have eaten two out of eight slices, or two-eighths of the pie.

The following circle represents our pie. You can see that the circle is divided into eight equal slices. Two of those slices are shaded. The shaded area is two-eighths of the pie, which can be written as .

Defining a Fraction

Every fraction is made up of two numbers with a horizontal line between them. The top number is called the numerator. The bottom number is called the denominator. In the fraction , the numerator is 2 and the denominator is 8. The numerator of a fraction can be any number, including zero, but the denominator of a fraction can never be zero. A fraction with a denominator of zero is undefined.

Fuel for Thought

A fraction represents a part of a whole. A fraction itself is a division statement. The top number of the fraction, the numerator, is divided by the bottom number of the fraction, the denominator.

The denominator is the number of parts that make the whole. Look again at our pie. There are 8 parts, or slices, that make up the whole. If the pie had only 4 slices, then the denominator of our fraction would be 4. The numerator is the number of parts that are shaded. Because our pie has 2 slices shaded, the numerator of our fraction is 2. The numerator always tells us how many parts of the whole we have.

Look at the following fraction. What fraction of this circle is shaded?

Defining a Fraction

There are 3 parts of the circle that are shaded. The numerator of our fraction will be 3. This circle is divided into only 6 equal parts, so the denominator of our fraction will be 6. Because there are 3 parts that are shaded out of 6 total parts, we can say that of the circle is shaded.

We just saw how to turn pictures (shaded circles) into fractions. Now let's go in the opposite direction: Let's draw pictures to represent fractions.

When you look at a fraction, read it as "the numerator out of the denominator." The fraction is "2 out of 4." To represent the fraction with a circle, we need to show 2 out of 4 parts shaded. First, draw a circle divided into 4 equal parts. Then, shade 2 of those parts:

Defining a Fraction

Pace Yourself

Fractions help us describe everyday situations. If you have 15 math problems for homework, and you've completed 5 of them, what fraction of your math homework is complete? The answer: 5 out of 15, or .

If of your class has brown hair, and there are 25 students in your class, how many have brown hair? Because the fraction means "12 out of 25," there are 12 students in your class with brown hair.

Find three other real-life scenarios that could be described with fractions.

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