Fractions

In everyday situations, there are many instances where we need only a part of something and not the entire object. For example, this happens when we share a pizza, cut a cake, or eat an apple. In the world of math, we need numbers to show these parts, and this is where the concept of fractions comes into play.

What is a Fraction?

Fractions represent a part of the whole, where the whole can be an object or a collection. For writing a fraction, it is necessary that all parts of the whole are equal.

Fraction is derived from the Latin word 'fractio,' meaning 'to break,' as fractions represent how something is divided. Imagine dividing a pizza into slices; each slice is a fraction of the whole pizza. The ancient Egyptians were the trailblazers of fractions. They used fractions in practical situations such as sharing food and resources. Their understanding of fractions paved the way for the mathematical concept we know today.

To gain a clearer perspective on fractions, let's examine the example given below. We can partition the whole into any number of equal parts. Each part signifies a fraction of the complete whole.

A whole can be divided into any number of equal parts and each part is a fraction of the whole.

Parts of a Fraction

A fraction has two parts: the numerator and denominator, which are separated by a horizontal line called a fraction bar.

The number written above the fraction bar is called the Numerator. The numerator signifies how many equal parts of the whole or collection are taken.

The number below the fraction bar is called the Denominator. The denominator signifies the total number of equal parts the whole is divided into or the total number of the same objects in a collection.

Take the example of the cake divided into 4 equal parts.

If we take one part of the cake, then it can be expressed as and if we take 3 parts of the cake, then it is expressed as .

Fraction of a Whole

Fractions of a whole tell us how many parts of a whole we talk about.

Imagine we have a delicious pizza in front of us, cut into eight equal slices. Each slice represents a fraction of the whole pizza. If we take two slices, we are essentially enjoying of the entire pizza. In this scenario, the whole pizza serves as the reference point, and the fraction depicts the specific portion we have chosen.

Fraction of a Collection

Fraction of a collection represents the number of equal parts from a collection of objects that we choose.

Let us consider a box of colorful marbles. Among the marbles, six are red and four are blue. The fraction of red marbles within the collection is , as there are six red marbles out of a total of ten marbles. Similarly, the fraction of blue marbles is . These fractions give a clear representation of the proportion of each type of marble within the collection.

Fractions on a Number Line

Like numbers, fractions can also be placed on the number line. Visualizing fractions on a number line offers insights into their magnitudes. When plotted, fractions help us understand their relationships to whole numbers and other fractions, providing a visual representation of their sizes.

By dividing the number line into equal portions, typically from 0 to 1, fractions can be accurately depicted. The denominator of the fraction designates the count of divisions on the number line. For instance, to illustrate , the number line is divided into five equal parts from 0 to 1. The initial division marks , followed by and . Notice that the final interval is, signifying 1 as the whole.

Below, observe a visual representation of these fractional points on a number line.

Types of fractions

Based on the numerator and denominator, fractions can be classified into different types, which are listed below-

Real-world Application of Fractions

Just like whole numbers, fractions too are very useful in day to day life. Here's a glimpse of how fractions come into play in the real world:

• Cooking and Baking : Recipes often call for fractions to achieve precise measurements of ingredients, from adding teaspoon of salt to cup of flour.
• Measurement : Lengths, areas, and volumes are frequently expressed as fractions, ensuring accuracy in carpentry, construction, and engineering.
• Currency and Finance : Fractions are integral in handling money, understanding interest rates, and calculating discounts.
• Medical Dosages : Accurate medication dosages, often in fractional units, are essential in healthcare to ensure patient safety.
• Art and Design : In art, fractions guide the placement of elements and proportions, while designers use fractions to create layouts.
• Sports and Fitness : Fractions determine sports statistics, such as scoring percentages in basketball or calculating BMI (Body Mass Index).
• Music : Musical notes and rhythms are expressed as fractions, dictating the duration and timing of sounds.

In essence, fractions are everywhere, enriching our understanding of quantities, proportions, and divisions in the world around us.