Understanding Fractions

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A fraction is used to represent equal parts of a whole body. There are fractions around us, from the fridge to a clock on the wall. While performing our daily activities, we use fractions unknowingly in several ways. You might have heard yourself say, “We’re having lunch at a quarter past one”, or “we need 1/3 of a cup of sugar for the cake.” Mastery of fractions is an important foundation for understanding advanced mathematics. Fractions are a student’s initial introduction to abstraction in mathematics. In this article, let us learn about fractions in detail.

What Is a Fraction?

A fraction is a term in mathematics used to describe parts of a whole. It is denoted by the ‘/’ symbol, such as a/b. The term fraction stemmed from the Latin word “fractus”, which means “broken.”

Fraction Definition

A fraction is defined as a number describing a portion of a whole. The whole can be an object or a group of objects, and the parts must be equal.

Let us understand the definition better with an example.

Consider the fraction 4/8. We read this as “four-eighths.”

“8” is the equal number of parts into which the whole is divided.

“4” is the number of equal parts taken out.

Fraction Representation

A fraction can be expressed in 3 ways: a fraction, a percentage, or a decimal.

Let us understand each of these forms of representation with the help of an example.

Fractional Representation

Fractional representation is the most common form of representing a fraction as a/b, where “a” is the numerator, and “b” is the denominator. The numerator and denominator are separated by a horizontal bar. In the sense of division, a can be named as a dividend, and b can be referred to as a divisor.

Example:

Consider the fraction 3/4; here, 3 is the numerator, and 4 is the denominator.

Decimal Representation

This format represents the fraction as a decimal number.

Example:

The fraction 2/4 can be represented in decimal form by dividing the numerator (2) by the denominator (4) (2/4 =0.5)

Percentage representation

The fraction is multiplied by 100 and converted into a percentage in this format.

Example:

Consider the fraction 2/4 and multiply it by 100 and convert it into a percentage as follows:

(2/4*100) = 50 %

Types of Fraction

As discussed in the previous section, the primary parts of a fraction are the numerator and denominator. Based on these, different types of fractions can be defined as follows:

Fraction Type Definition Example
Proper Fraction Fractions in which the numerator is smaller than the denominator. 3/7

 

Improper Fraction Fractions in which the numerator is greater than the denominator. 7/3
Mixed Fraction Fraction that consists of a whole number, along with a proper fraction. [latex]2\frac{3}{7}[/latex]
Like Fraction Two or more fractions that have the same denominator. 7/3 and 2/3
Unlike Fraction Two or more fractions with different denominators. 4/6 and 5/3

Operations on Fractions

Addition of Fractions

Adding Like Fractions

To add like fractions, add the values of the numerator, keeping the denominator the same.

Example:

 ⅗+⅕ = (3+1)/5 = ⅘

Adding Unlike Fractions

To add unlike fractions, we need to follow the below steps:

  • Find the LCM of the denominator.
  • Change the denominator into the obtained LCM.
  • Now, add the numerators.

Example:

4/7 + 2/3

The LCM of (7,3) is 21

Equalise the denominator and simplify further as follows:

12/21+14/21=(12+14)/21=26/21

Subtraction of Fractions

Subtracting Like Fractions

To subtract like fractions, subtract the values of the numerator, keeping the denominator same.

⅗-⅕=⅖

Subtracting Unlike Fractions

To subtract unlike fractions, we need to follow the below steps:

  • Find the LCM of the denominator.
  • Change the denominator into the obtained LCM.
  • Now, subtract the numerators.

Example:

4/7 – 2/3

The LCM of (7,3) is 21

Equalise the denominator and simplify further as follows:

4/7 – 2/3 = -2/21

Multiplication of Fractions

Multiplication of fractions involves multiplying the numerators and denominators separately.

The first fraction’s numerator will be multiplied by the second’s numerator, and the first fraction’s denominator will be multiplied by the second’s.

The product fraction will be reduced to its lowest form if required.

Example:

2/3 × 2/1  = 4/3

Division and Reciprocity of Fractions

Division of fractions involves multiplying the first fraction by the reciprocal of the second fraction. When the numerator and denominator of a fraction are interchanged, then it is said to be reciprocal. Suppose a fraction is a/b; then, its reciprocal will be b/a. The division of fractions involves the following steps:

  • Determine the reciprocal of the second fraction.
  • Multiply the reciprocal of the second fraction with the first fraction.
  • Find the simplified fraction if required.

Example:

4/15 ÷ 2/3

4/15 × 3/2 = 12/30

Simplifying the fraction further, we get

4/15 × 3/2 = 2/5

What Is the Purpose of Fractions?

Some applications of fractions in real-life situations are as follows:

  • The waitress brings only one bill when you go to a restaurant with friends. To divide the total amongst your friends, you use fractions.
  • When you instruct a carpenter to build a table, you specify dimensions such as seven feet, three and half a quarter inches. The carpenter employs the fraction concept to break down the measurement and cut the wood according to the requirements. With the idea of fractions, it is possible to carry out such measures.
  • A recipe for two people suggests using 3/4 teaspoon sugar and 1/2  tablespoon salt. To adjust the same recipe for three people, we use fractions.