Fractions

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word 'fractio' which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.

In Ancient Rome, fractions were only written using words to describe a part of the whole. In India, the fractions were first written with one number above another (numerator and denominator), but without a line known as the fraction bar. It was the Arabs, who added the line which is used to separate the numerator and the denominator. Let us learn more about fractions, and fraction examples, along with a few fraction practice problems.

What are Fractions?

Fractions, in Mathematics, are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing. Let us understand this concept using an example. The following figure shows a pizza that is divided into 4 equal parts. Now, if we want to express one selected part of the pizza, we can express it as 1/4 which shows that out of 4 equal parts, we are referring to 1 part.

It means one in four equal parts. It can also be read as:

One-fourth, or 1 by 4

If we select 2 parts of the pizza, it will be expressed as 2/4. Similarly, if we are referring to 3 parts of this pizza, we would write it as 3/4 as a fraction.

Fraction Definition

Fraction is defined as a part of something, and a quantity that is not a whole number. It is expressed as the number of equal parts being counted over the total number of parts in the whole.

Fraction Bar

Fraction bar is the line that is drawn to separate the numerator and the denominator. Let us learn more about the parts of a fraction in the following section.

Parts of a Fraction

All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fraction bar.

The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.

The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.

Types of Fractions

Based on the numerator and denominator, which are parts of a fraction, there are different types of fractions as listed below:

Proper Fraction

Proper fractions are the fractions in which the numerator is less than its denominator. For example, 5/7, 3/8, 2/5, and so on are proper fractions.

Improper Fraction

An improper fraction is the type of fraction in which the numerator is more than or equal to its denominator. It is always the same or greater than the whole. For example, 4/3, 5/2, 8/5, and so on.

Unit Fraction

Fractions in which the numerator is 1 are known as unit fractions. For example, 1/4, 1/7, 1/9, and so on.

Mixed Fraction

A mixed fraction is a mixture of a whole number and a proper fraction. For example,

5 1/3 , where 5 is the whole number and 1/3 is the proper fraction, or, 2 2/5, 7 9/11, and so on.

Equivalent Fraction

Equivalent fractions are the fractions that represent the same value after they are simplified. To get equivalent fractions of any given fraction:

We can multiply both the numerator and the denominator of the given fraction by the same number.

We can divide both the numerator and the denominator of the given fraction by the same number.

Example: Find the two fractions that are equivalent to 5/7.

Solution:

Equivalent Fraction 1: Let us multiply the numerator and the denominator with the same number 2. This means, 5/7= (5 × 2)/(7 × 2) = 10/14

Equivalent Fraction 2: Let us multiply the numerator and the denominator with the same number 3. This means, 5/7 = (5 × 3)/(7 × 3) = 15/21

Therefore, 10/14, 15/21, and 5/7 are equivalent fractions.

Like and Unlike Fractions

Like fractions are the fractions that have the same denominators. For example, 5/15, 3/15, 17/15, and 31/15 are like fractions.

Unlike fractions are the fractions which have different denominators. For example, 2/7, 9/11, 3/13, and 39/46 are unlike fractions.

Fraction on a Number Line

The representation of fractions on a number line demonstrates the intervals between two integers, which also shows us the fundamental principle of fractional number creation. The fractions on a number line can be represented by making equal parts of a whole, i.e., from 0 to 1. The denominator of the fraction would represent the number of equal parts in which the number line will be divided and marked. For example, if we need to represent 1/8 on the number line, we need to mark 0 and 1 on the two ends and divide the number line into 8 equal parts. Then, the first interval can be marked as 1/8. Similarly, the next interval can be marked as 2/8, the next one can be marked as 3/8, and so on. It should be noted that the last interval represents 8/8 which means 1. Observe the following number line that represents these fractions on a number line.