Fractions

What is a 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 means, broken. An excellent real-life example of the fraction can be that of a pizza when cut into six equal pieces. Here, since the pizza 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 pizza. 

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  \[\dfrac{3}{5}\], and the boys will be \[\dfrac{2}{5}\]. 

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 into 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

Fractions are further broken down into various categories based on the characteristics of the numerator and denominator. As follows:

• Proper Fractions: In these fractions, the numerator is less than the denominator. An example of such a fraction is \[\dfrac{2}{3}\], where the numerator (2) < denominator(3). 

• Improper Fractions: In these fractions, the numerator is greater than the denominator. For example - \[\dfrac{3}{2}\]. where the numerator (3) > denominator (2). 

• Like Fractions: The group of two or more fractions that have exactly the same denominator or we can say that the fractions which have the same numbers in the denominators are called like fractions. For example, \[\dfrac{1}{13}\], \[\dfrac{4}{13}\], and \[\dfrac{3}{13}\] are all like fractions, whose denominators are equal to 8.

• Unlike fractions: Fractions with different denominators are called, unlike fractions. The denominators of fractions have different values. For example, \[\dfrac{3}{2}\], \[\dfrac{3}{4}\], \[\dfrac{5}{6}\], \[\dfrac{7}{9}\] are unlike fractions.

• Mixed Fractions: A mixed fraction is obtained by adding a non-zero integer and a proper fraction. Some examples are: \[2\dfrac{1}{4}\],\[3\dfrac{3}{7}\].

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 with the same denominators, to find the sum or difference of the fractions, you can add or subtract both numerators without changing the denominator.
  Example: For adding  \[\dfrac{4}{9}\] +  \[\dfrac{8}{9}\], you can keep the denominators the same and write the sum of 4+8 = 12 as the numerator of the new fraction,  \[\dfrac{12}{9}\]. 

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

For adding  \[\dfrac{1}{3}\]  +   \[\dfrac{1}{6}\], the LCM or Lowest Common Multiple  is 2.

Therefore,  \[\dfrac{1\times 2}{3\times 2}\]=  \[\dfrac{2}{6}\]

Now when  \[\dfrac{2}{6}\] is added to  \[\dfrac{1}{6}\] =  \[\dfrac{3}{6}\].

Converting Fractions to Decimals

Fractions can easily be converted into decimals when the numerator is divided by the denominator. For example, The fraction \[\dfrac{1}{2}\] can be represented as decimal 0.5, since 1 divided by 2 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   \[\dfrac{25}{100}\], 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 =   \[\dfrac{4}{100}\]

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'.