 # Fractions

## What is Fraction?

Fractions represent any number of equal parts in a whole number. It is shown in the form of '/', as in, a/b. The number on the top is known as the ‘numerator’, and the number below is known as the ‘denominator’. Derived from the original Latin word 'Fractus,' the term fraction meaning, broken. An excellent real-life example of fraction can be that of a pizza when cut into six equal pieces. Here, since the pie was one or whole and then further divided into six parts, the fraction formula of each part would be 1/6, where 1 represents a part of the whole of the pie, and 6 represents the number of divided sections. We would term the fraction as one-sixth of the pie.

### What is the Definition of Fractions?

A fraction simply tells us how many parts of a whole number are there in reference to a problem. It can be understood in the following fraction definition and example:

If there are 5 children, out of which 3 are girls, and 2 are boys. Then the corresponding fraction for girls will be 3/5, and the boys will be 2/5.

It is essential to understand the concept of fractions properly as these are widely used in mathematics and real life.

### What is A Fraction in Real-life?

Learning about fractions may also interest you in real life applications of it. When you slice your birthday cake into equal pieces, it represents a fraction. So, let’s say that you have four friends and you cut the birthday cake in 4 equal parts. If you take one slice of it, you will be taking 1/4th of the cake and leaving the remaining 3/4th for your friends.

### Types of Fractions

There are six different types of fractions. Based on the properties of a fraction, here are some with examples:

• Proper Fractions: In these fractions, the numerator is lesser in value than the denominator. An example about such a fraction is 2/3, where numerator 2 < denominator 3.

• Improper Fractions: In these fractions, the numerator is greater than the denominator. For example - 3/2. where numerator 3 > denominator 2.

• Like Fractions: For fractions that are alike or can be simplified to get the same fraction are called fractions. For example:

What is the like fraction of 2/4 in math? It is 1/2 since the numerator and denominator have 2 as their common divisor.

• Mixed Fractions: A mixed fraction is obtained by adding a non-zero integer and a proper fraction. Some examples are:

### How To Understand Addition and Subtraction of Fractions?

For a quick understanding of addition and subtractions in fractions, you need to keep in mind the following rules:

• For fractions having the same denominators, to find the sum or difference of the fractions, you can just add or subtract both the numerators without changing the denominator.

Example: For adding 4/9 + 8/9, you can keep the denominators the same and write the sum of 4+8 = 12 as the numerator of the new fraction, 12/9.

• For fractions having different denominators, you need to find out the LCM (Lowest Common Multiple)  for the denominators. Then you need to multiply both numerator and denominator by the same amount to keep the denominators of both the fractions the same. Once multiplied, you can then add the product of one numerator to the other in the new fraction.

For adding 1/3  +  1/6, the LCM or Lowest Common Multiple  is 2.

Therefore, 1 x 2/3 x 2 = 2/6

Now when 2/6 is added to 1/6 = 3/6.

### Converting Fractions to Decimals

Fractions can easily be converted into decimals when the numerator is divided by the denominator. For example, The fraction 1/2 can be represented as decimal 0.5, since 2 divided by 1 gives 0.5 as the answer.

Similarly, for converting decimals to fractions, you can just arrange the numbers beyond the decimal point as the numerator, with the number of places of zeroes as the denominator. For example, 0.25 can be represented as 25/100, as the number of places beyond the decimal is 2. So, you can add two zeros, following the digit ‘1’ in the fractional representation of the denominator.

### Sample Fraction Questions with Answers:

Question 1: Convert 0.04 into a fraction.

Answer: For starters, we can write the digit 1 in the denominator for the fractional representation of 0.04

Now, for the decimal 0.04, you need to count the number of decimal places beyond the decimal.

Since in 0.04, the digits 0 and 4 come two places after the decimal, therefore you need two zeroes in the denominator.

The fractional representation would be =  4/100

Numerator = The whole digits present in the decimal numbers i.e., 4

Denominator = Digit one, followed by zeros based on the number of decimal places present in the decimal number, i.e., two. Therefore, the denominator would be '100'.

1. Can a fraction have a 0 or 1 in its denominator?

Answer: A fraction can have ‘1’ in its denominator, but then they are called Unit Fractions, since they represent the whole number itself, without any divisions.

For example: Fraction 3/1, represents the whole number 3 without any equally divided parts. Therefore, these are called unit fractions.

A fraction cannot have ‘0’ in its denominator since the value of such fractions would only be undefined or ∞.

This means 2/0, -6/0. 0.54/7-7 are not legal fractions because their values are all undefined, and therefore considered meaningless. Anytime you encounter any such fractions, know that they don’t have any computable value, and therefore are unnecessary in any equation.

2. Are all fractions rational numbers?

Rational numbers can be defined in the form of a/b, where a and b are integers with b not equal to 0.

There are several fractions that have numerator and denominators as irrational or cannot be defined as a ratio between two integers, a and b.

For example: √3/4, π/8, etc are all irrational fractions.

Here π = 3.1415926535897932384626433832795.. and is an irrational number that cannot be represented as a fraction between two integers. 22/7 is a widely used approximation.

Similarly, √3 has a value of 1.73205080756887729352, which cannot be represented as a fraction.

Therefore, not all fractions are rational numbers; but all rational numbers can be defined in fractions.