Fractions

The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, learnt 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. It was the Arabs only, who added the line which is used to separate the numerator and the denominator.

Table of Contents


What are Fractions?

In Mathematics, fractions are represented as numerical value, can be defined as the parts 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. Here's a pizza which is divided into 8 equal parts. Do you know what 1/8 means?

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

  • One-eighth, or
  • 1 by 8

 

1/8 = one in eight equal parts

This is called a fraction.

Parts of a Fraction

All fractions consist of a numerator and a denominator.

  • The denominator indicates how many parts the whole has been divided into. It is placed in the lower part of the fraction.
  • The numerator indicates how many sections of the fraction are represented. It is placed in the upper part of the whole.

Types of Fractions

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

Proper Fraction

Proper fractions are the fractions in which the numerator is less than its denominator. It is often smaller than the whole. Example: 5/7, 3/8, 2/5, etc.

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. Example: 4/3, 5/2, 8/5, etc.

Unit Fraction

Fractions with numerator as 1 are known as unit fractions. Example: 1/4, 1/7, 1/9, etc.

Mixed Fraction

A mixed fraction is a mixture of a whole and a proper fraction. Example: \(5\frac{1}{3}\)\(2\frac{2}{5}\)\(7\frac{9}{11}\), etc.

Equivalent Fraction

Equivalent fractions are the fractions that represent the same value. It's the same portion of a whole. To get equivalent fractions of any given fraction:

  • We can multiply both the numerator as well as the denominator of the given fraction by the same number.
  • And for division, we can divide both the numerator and the denominator of the given fraction by the same number.

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

Solution:

Equivalent Fraction 1: 5/7= 5/7 x 2/2 = 10/14

Equivalent Fraction 2: 5/7 = 5/7 x 3/3 = 15/21

Like and Unlike Fractions

Like fractions are the fractions that have the same denominators. Example: 5/15, 3/15, 17/15, and 31/15.

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

Fractions on a Number Line

The representation of fractions on a number line demonstrates the intervals between two integers, which also show us the fundamental principle of fractional number creation.

Example: Let's represent the fractions: 2/11, 7/11, -8/11, and -3/11 on a number line.

Solution: 

Since the denominator of each given fraction is 11, we can divide the space between every pair of two consecutive integers (on the number line) into 11 equal parts.

Each part will represent the fraction 1/11 on the number line. 

  • To mark 2/11, move two parts to the right of zero.
  • To mark 7/11, move seven parts to the right of zero.
  • To mark -8/11, move eight parts to the left of zero.
  • To mark -3/11, move three parts to the left of zero.

Hence, the markings of fractions on the number line will be in the sequence: -8/11, -3/11, 2/11, and 7/11. 

Fractions on Number Line: -8/11, -3/11, 2/11, and 7/11

Note: The markings on the number line are just for showing the order of fractions. These are not the actual number gaps. 


Important Topics

Given below is the list of topics that are closely connected to fractions. These topics will also give you a glimpse of how such concepts are covered in Cuemath.


FAQs on Fractions

What is 0.125 as a Fraction?

0.125 as fraction can be written as, 1/8. Here's how, we can find out: 125/1000 = 5/40 = 1/8

What is the Unit Fraction of 5/8?

The unit fraction 5/8 is the same as the unit fraction 1/8 represented five times.

How are Fractions and Decimals Related?

Both fractions and decimals are just ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part is connected through a decimal, for example, 0.50. 

How do you Simplify Fractions?

In order to simplify a fraction. First, write down the factors for the numerator and the denominator. Then, determine the largest factor that is common between the two and divide the numerator and denominator by the greatest common factor. You will get a reduced fraction, that is, the simplest form of the given fraction. For example, 36/45 (gcf = 9) = 4/5

How to Multiply Fractions?

To multiply the two fractions, multiply the numerators, multiply the denominators. Then, simplify the resultant fraction. For example, 3/5 x 15/18 = 45/90 = 1/2.

How to Divide Fractions?

To divide one fraction by another, multiply the first fraction with the reciprocal of the second fraction. Then, multiply the numerators, multiply the  denominators. Then, simplify the resultant fraction, if required. For example, 5/6 ÷ 1/5 = 5/6 x 5/1 = 1/6.

What do you call Fractions with the Same Denominator?

Fractions with the same denominator are known as like fractions.

How do you Determine which Fraction is Greater?

To determine, which fraction is greater, compare the denominators:

  • In case of different, rewrite one or more fractions with a common denominator.
  • In case of the same denominators, the fraction with the greater numerator is the greater fraction.

Are all Fractions Less Than 1?

No, all fractions are not less than 1. Let's have a look!

  • Proper fractions are greater than 0 but less than 1. (The numerator is less than the denominator) 
  • Improper fractions are always 1 or greater than 1. (The numerator is greater than or equal to the denominator)

Solved Examples on Fractions

Example 1: Milk is sold at $16 per gallon. Find the cost of \(6\dfrac{2}{5}\) gallons of milk.

Solution:

Cost of one gallon of milk = $16

Therefore, the cost of \(6\dfrac{2}{5}\) gallons i.e. 32/5 gallons will be 32/5 * 16 = $102.4

Therefore, the cost of gallons of milk is $102.4

Example 2: In a class of 48 students, 1/4 of them watch cartoons. How many students do not watch cartoons?

Solution:

Total number of students = 48

Number of students who watch cartoons = 1/4 x 48 = 12

Thus, the number of students who don't watch cartoons = 48 - 12 = 36

Therefore, the number of students who do not watch cartoons is 36

Example 3: The snowfall during the first three months in winter was 30.5 inches, 45.25 inches, and 25.25 inches. What was the total amount of snow in these months?

Solution:

Total amount of snow for three months = 30.5 + 45.25 + 25.25

                                                              = 305/10 + 452.5/10 + 252.5/10

                                                              = (305 + 452.5 + 252.5)/10 = 1010

                                                              =1010/10 = 101inches

Therefore, the total amount of snow in 3 months was 101 inches.

Practice Questions on Fractions

Here are a few activities for you to practice.

Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
  
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus