Introduction

In this lesson, you will learn about fractions and what they represent out of a whole number.

Quick Tip

This is where the forward slash (/) means division. Fractions can be written as \(\frac{5}{7}\), \({5}/{7}\), or they might be written as \(5\div 7\). You may see them written either way in this course.

This video illustrates the lesson material below. Watching the video is optional.

• Introduction to Fractions (04:10 mins) | Transcript

Numerator and Denominator

Fractions are just another way to represent division. For example, \(5\div7\) is the same as \(\frac{5}{7}\) and \({5}/{7}\). So \(\frac{5}{7}\) and \({5}/{7}\) are the fraction forms of \(5\div7\). You can call it five-sevenths, five divided by seven, or five over seven. The number above the line is the numerator, and the number below the line is the denominator.
\begin{align} {5}\div {7}\ = \frac{5}{7} \end{align}

The top part of a fraction is called the numerator, and the bottom part is called the denominator. Remember, a fraction isn't a whole number, it represents part of a whole.

In the fraction \(\frac{5}{7}\), the denominator tells you that you need seven pieces to make one whole. The numerator tells you how many of those pieces you have. Another way to think of the denominator is to think of it as a representation of the size of the pieces that you have.

Fraction Examples

Look at this shape, which has been divided into five equal parts. Each individual part can be described as \(\frac{1}{5}\) (pronounced one-fifth) of the entire shape.

Figure 1

If you divide the same shape into twelve parts, you can see that each part is smaller than before when you only had five pieces. In this case, each part is \(\frac{1}{12}\) or one-twelfth of the entire shape.

Figure 2

In this example, the shape has been divided into twelve parts, but this time you've shaded three of those pieces. These three pieces can be represented as three out of twelve or \(\frac{3}{12}\).

Figure 3

With three twelfths shaded, there are nine-twelfths still remaining.

So far you've used shapes to help you understand fractions, but another way to represent fractions is through divided lines.

This line has been divided into six equal parts. Each segment is the same length. You can say the first segment is one out of six parts or one-sixth of the whole. If you put multiple segments together, you have \(\frac{2}{6}\), \(\frac{3}{6}\) , \(\frac{4}{6}\), and so forth. The whole line is the same as if you have six of the six segments, which equals one whole.

Figure 4

Another way to think of fractions is as part of a set. For example, consider a box of crayons.

Figure 5

The entire box is made up of seven crayons, so each crayon is one out of seven. If you take three of these crayons and give them to a friend, how many will remain out of seven?

Figure 6

You have taken three out of the seven crayons, or \(\frac{3}{7}\) of the crayons, and given them away. This leaves you with \(\frac{4}{7}\) of the crayons remaining. You have four-sevenths because, in this case, a full box still takes seven crayons but your friend has three of the seven.

Things to Remember

• Fractions are just another way to represent division.
• The numerator is on top of the fraction and the denominator is at the bottom. The denominator describes the number of pieces it takes to make one whole piece.
• A fraction is the same thing as saying a number is divided by another number. For example, two divided by five is the same thing as two out of five.

Practice Problems

1. In the fraction \(\dfrac{2}{3}\), what is the numerator and what is the denominator? (

Solution

x

Solution: The numerator is 2, and the denominator is 3.
Details: The numerator is the number on the top of the fraction. The denominator is the number on the bottom of the fraction. In this case, the numerator is 2, and the denominator is 3.
\begin{align} \frac{2}{3} \end{align}

)
2. Suppose you invited seven friends to a party and five of them attended. Give a fraction that represents the proportion of your friends who attended the party. (

Video Solution

x

Solution: \(\dfrac{5}{7}\)
Details:

(Introduction to Fractions #2 (01:17 mins) | Transcript)

| Transcript)
3. What fraction of the whole does the shaded portion represent?

(

Video Solution

x

Solution: \(\dfrac{5}{8}\)
Details:

(Introduction to Fractions #3 (00:50 mins) | Transcript)

| Transcript)
4. What fraction of the whole does the shaded portion represent?

(

Solution

x

Solution: \(\dfrac{2}{3}\)
Details:
The whole shape is divided into 3 parts. Two of those parts are shaded. You can think of a fraction in the following way:

\(\displaystyle \frac{\text{The number of parts you have}}{\text{The number of parts to make a whole}}\)

So, in this case, the fraction is \(\dfrac{2}{3}\).

)

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