Fractions - Definition, Types & Examples

Fractions: In mathematics, students often wonder what is fraction and why it is useful. A fraction is a number that shows a part of a whole. It helps us understand how much we have when something is divided into equal parts.

For example, if an apple is cut into 4 equal pieces and 1 piece is taken, then 1 out of 4 parts is left. This can be written as ¼ in the form of a fraction. Fractions not only help in solving maths problems but also in sharing, measuring, and dividing things equally in daily life.

Read More: Division of Fractions

Fraction Definition and Examples

A fraction is a way to show a part of something whole. It tells us how many parts we have compared to the total number of equal parts. Therefore, to define what is fraction in simple words, it can be said that fraction is a mathematical expression that represents one or more parts of a whole. It is written in the form a/b, where:

• a is the numerator, showing how many parts are taken.

• b is the denominator, showing the total number of equal parts the whole is divided into.

• The line that separates them is called the fraction bar.

Fractions Examples:

• 1/2: If a roti is cut into 2 equal pieces and you eat one, you’ve eaten half or 1/2, of it.

• 3/4: If a chocolate is divided into 4 pieces and someone eats 3, they’ve eaten 3/4 of the chocolate.

• 5/8: If a ribbon is split into 8 parts and you take 5, you have 5/8 of the ribbon.

Read More: 30 Fun Maths Questions with Answers

Understanding Parts of a Fraction

A fraction is made up of three important parts that help us know how much we have out of a whole. These parts are:

1. Numerator

The number written on the top of a fraction is called the numerator. It shows how many parts are taken or being counted.

2. Denominator

The number written at the bottom is called the denominator. It tells us how many equal parts the whole is divided into.

3. Fraction Line (Vinculum)

The line that separates the top and bottom numbers is known as the fraction line or vinculum. It shows that the number is written in fraction form.

For example, iIn the fraction 3/5:

• 3 is the numerator (3 parts taken).

• 5 is the denominator (the whole is divided into 5 parts).

• The line between them is the fraction line.

Also Read: Skip Counting

Types of Fractions in Maths

In maths, there are different types of fractions depending on how the number on top (which is called the numerator) and the number on the bottom (which is the denominator) are arranged. Let's explain the main types of fractions one by one:

1. Proper Fractions

A proper fraction is when the numerator is smaller than the denominator. For example, 3/5 is a proper fraction because 3 is less than 5. These fractions are always less than 1.

2. Improper Fractions

An improper fraction has the top number equal to or greater than the bottom number. For instance, 7/4 is an improper fraction because 7 is more than 4. These fractions are equal to or more than 1.

3. Mixed Fractions

A mixed fraction is made up of a whole number and a proper fraction. For example, 2 1⁄2 means 2 wholes and 1 part out of 2. It is always more than 1.

4. Unit Fractions

When the numerator is 1, it is called a unit fraction. For example, 1/9 or 1/3. These show only one part of the whole.

5. Like Fractions

Like fractions have the same denominator. For example, 2/7 and 5/7 are like fractions because both have 7 in the denominator.

6. Unlike Fractions

Unlike fractions have different denominators. For example, 1/3 and 2/5 are unlike because the denominators are not the same.

7. Equivalent Fractions

Equivalent fractions may look different, but they have the same value when simplified. For example, 1/2 and 2/4 are equivalent fractions because they represent the same amount.

Fractions on a Number Line

A number line is a straight line that shows numbers in order. Just like we show whole numbers like 0, 1, 2, 3, and 4 on a number line, we can also show fractions between these numbers.

To show a fraction on a number line, we divide the space between two whole numbers into equal parts. The number of parts depends on the denominator. The numerator tells us how many parts we have from those. 

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How to Show Fractions on a Number Line?

We can follow these simple steps to show any fraction on a number line:

• Step 1: Draw a straight number line.

• Step 2: Look at the fraction number given.

• If it is a proper fraction like 2/3, mark 0 and 1 on the line.

• If it is an improper fraction like 5/3, change it to a mixed number first (5/3 = 1 2/3), and then mark the whole numbers between which it falls. For 1 2/3, you’ll mark 1 and 2.

• Step 3: Divide the space between the two whole numbers into equal parts, based on the denominator of the fraction. For example, if the fraction is 3/4, divide the space from 0 to 1 into 4 equal parts.

• Step 4: Starting from the left, count the number of parts shown by the numerator.
  If it’s 3/4, count 3 parts from 0.

• Step 5: Mark the point. That is the position of the fraction on the number line.

Also Read: Types of Line in Math

Different Properties of Fractions

Fractions follow some special rules in maths, just like whole numbers do. These are called the properties of fractions. These rules help us add, multiply, and work with fractions more easily.

1. Commutative Property (for Addition and Multiplication)

This rule says that while adding fractions or multiplying two fractions, it doesn’t matter which one comes first; the answer will still be the same. For example:

• Addition: 1/3 + 2/5 = 2/5 + 1/3

• Multiplication: 2/7 × 3/4 = 3/4 × 2/7

2. Associative Property (for Addition and Multiplication)

This property tells us that even if we group the fractions differently, the result will not change when we add or multiply them. For example:

• Addition: (1/2 + 1/4) + 1/8 = 1/2 + (1/4 + 1/8)

• Multiplication: (2/3 × 3/5) × 4/7 = 2/3 × (3/5 × 4/7)

3. Identity Property

This property shows that when we add 0 to any fraction, the value stays the same. Also, during the multiplication of fractions by 1, the answer will also remain the same. For example:

• Addition: 5/6 + 0 = 5/6

• Multiplication: 3/4 × 1 = 3/4

4. Multiplicative Inverse (Reciprocal Property)

Every fraction has a reciprocal. When we multiply a fraction by its reciprocal, the answer is always 1. For example:

• 2/3 × 3/2 = 1

5. Distributive Property

This rule is useful when we multiply a fraction with the sum of two other fractions. We can multiply each one separately and then add. For example:

• 1/2 × (1/4 + 1/6) = 1/2 × 1/4 + 1/2 × ⅙

Interesting Facts About Fractions

Fractions are not just a part of mathematics; they have an interesting history and are used in many places around us. Here are some fun and surprising facts about fractions:

• Fractions are ancient! People have been using fractions for thousands of years. Ancient Egyptians used them to divide land and share food.

• The word ‘fraction’ means ‘broken.’ It comes from the Latin word fractus, which shows that fractions represent broken or divided parts of a whole.

• Decimals are also fractions. Any number with a point, like 0.5 or 0.75, is actually a fraction. For example, 0.75 is the same as 3/4.

• Music uses fractions. In music, different notes have different lengths. A full note is 1, a half note is 1/2, a quarter note is 1/4, and so on.

• The line in a fraction has a name. The horizontal line that separates the top and bottom numbers in a fraction is called a vinculum. It shows the connection between both parts.

• Romans used a different way of writing fractions. They didn’t use fractions like we do now. They used a system based on twelfths, and that’s where the word ounce comes from!

• Some fractions never stop in decimal form. When we change fractions like 1/3 or 1/6 into decimals, the numbers keep repeating. For example, 1/3 = 0.333... and 1/6 = 0.1666...

• All fractions are rational numbers. A rational number is any number that can be written as one number divided by another. So, every fraction is a rational number.

• Percentages are also fractions. A percent means ‘out of 100.’ So, 50% is the same as 50/100 or 1/2, and 25% is the same as 25/100 or 1/4.

Read More: Cuboid

Fractions Practice Questions

1. What type of fraction is 3/7?

• a) Proper fraction

• b) Improper fraction

• c) Mixed number

• d) Whole number

2. Which of the following is an improper fraction?

• a) 2/5

• b) 4/4

• c) 7/3

• d) 3/10

3. Choose the mixed number from the options below:

• a) 6/2

• b) 2 1/4

• c) 1/3

• d) 5/5

4. What is the numerator in the fraction 5/8?

• a) 8

• b) 5

• c) 13

• d) None of these

5. Which of the following fractions is equal to 1?

• a) 2/3

• b) 3/3

• c) 5/4

• d) 1/2

6. In the fraction 9/4, how many whole parts and fraction parts are there?

• a) 2 wholes and 1/4

• b) 2 wholes and 2/4

• c) 1 whole and 3/4

• d) 3 wholes and 1/4

7. Which of the following is a proper fraction?

• a) 8/3

• b) 2/2

• c) 3/5

• d) 5/2

Answers:

1. a) Proper fraction (A proper fraction has a numerator smaller than the denominator.)

2. c) 7/3 (An improper fraction has a numerator greater than or equal to the denominator.)

3. b) 2 1/4 (A mixed number includes a whole number and a proper fraction.)

4. b) 5 (The numerator is the top number in a fraction.)

5. b) 3/3 (Any fraction where the numerator and denominator are equal is equal to 1.)

6. a) 2 wholes and 1/4 (9 ÷ 4 = 2 whole parts and 1 leftover, so 9/4 = 2 1/4.)

7. c) 3/5 (A proper fraction has the numerator less than the denominator)

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