In this video you will learn the basic set up of a fraction. Definition of numerator and denominator. Followed by easy, real-life examples.

For more help, check out our Introduction to Fractions Lesson Page

Credit goes to: Kids Learning Videos

## What is a Fraction?

A fraction is a mathematical representation of a part of a whole or a division of one quantity into equal parts. Fractions are used to express values that are not whole numbers, including numbers that are less than one. They consist of two main components:

**Numerator** – The numerator is the top part of a fraction, and it represents the number of parts you have or are considering. It is the dividend in a division problem. For example, in the fraction 3/5, the numerator is 3, indicating that there are 3 parts or items being considered.

**Denominator** – The denominator is the bottom part of a fraction, and it represents the total number of equal parts that make up the whole. It is the divisor in a division problem. In the fraction 3/5, the denominator is 5, indicating that the whole is divided into 5 equal parts.

The fraction is typically written in the form “N/D,” where N is the numerator and D is the denominator. Fractions can represent values that are greater than one (improper fractions) or values less than one (proper fractions) based on the relationship between the numerator and denominator.

### What Are the Types of Fractions?

**Proper Fraction** – A proper fraction is a fraction in which the numerator is smaller than the denominator. For example, 2/3, 1/4, and 3/7 are proper fractions.

**Improper Fraction** – An improper fraction is a fraction in which the numerator is equal to or greater than the denominator. For example, 7/4, 5/5, and 9/3 are improper fractions.

**Mixed Number **– A mixed number is a combination of a whole number and a proper fraction. It is written as a whole number followed by a proper fraction. For example, 2 1/3, 5 4/7, and 7 2/5 are mixed numbers.

**Unit Fraction** – A unit fraction is a fraction in which the numerator is 1. For example, 1/2, 1/3, and 1/10 are unit fractions.

Fractions are used in various mathematical operations, including addition, subtraction, multiplication, and division. They are also used in real-life situations to represent quantities that are not whole numbers, such as parts of a pizza, portions of time, or divisions of a quantity into equal shares. Understanding fractions is essential in mathematics and everyday problem-solving.

### Real World Examples of Fractions

**Pizza Slices**

Imagine you have a delicious pizza, and you want to share it with your friends. The pizza is divided into 8 equal slices. In this scenario:

- The whole pizza represents the whole, which can be expressed as 1.
- The number of slices you choose to eat or share is represented by the numerator. Let’s say you eat 3 slices, so the numerator is 3.
- The total number of equal slices in the pizza is represented by the denominator, which is 8 in this case.

Therefore, the fraction that represents the number of slices you ate is 3/8. This means you ate three out of the eight equal slices of the pizza.

**Time**

Consider a clock showing the time between 2:00 PM and 3:00 PM. You want to know what fraction of the day has passed by this time.

- The whole day consists of 24 hours, which can be represented as 1.
- The time between 2:00 PM and 3:00 PM is 1 hour.
- To find the fraction of the day that has passed, we use the numerator to represent the 1 hour, and the denominator remains 24 hours.

Therefore, the fraction representing the time that has passed is 1/24. This means that 1/24 of the day has elapsed between 2:00 PM and 3:00 PM.

**Liquid in a Container**

Suppose you have a glass of orange juice, and you want to determine how much of the glass is filled with juice.

- The full glass represents the whole, which can be expressed as 1.
- The volume of orange juice in the glass is represented by the numerator. Let’s say the glass is half-filled with juice, so the numerator is 1/2.
- The denominator remains 1 because it represents the entire glass.

Therefore, the fraction that represents the amount of orange juice in the glass is 1/2. This means that half of the glass is filled with orange juice.

In these real-life examples, fractions are used to represent parts of a whole or parts of a given quantity. They allow us to express and understand proportions, divisions, and relative amounts in various everyday situations, making them a fundamental concept in our daily lives and in mathematics.