How to Identify Proper, Improper, Mixed, Like & Unlike Fractions
In mathematics, fractions are categorised into three main types: proper fractions, improper fractions, and mixed fractions. A fraction is a term that consists of a numerator and a denominator, and its type is determined based on these two parts.
Fractions represent parts of a whole object. For example, if a pizza is cut into four equal slices, each slice is represented as 1/4 of the pizza. Here, the number 1 is the numerator, and 4 is the denominator.
In addition to the three main types of fractions, there are three more categories: like fractions, unlike fractions, and equivalent fractions. Therefore, there are a total of six types of fractions: proper fractions, improper fractions, mixed fractions, like fractions, unlike fractions, and equivalent fractions.
What is a Fraction?
A fraction is a portion of a whole object. The fraction indicates how many parts you have of anything when it is divided into several pieces. It is expressed as the number of equal parts counted (the numerator) divided by the total number of parts (the denominator).
Fraction
Types of Fractions with Examples
In Maths, there are three Different Types of Fractions They are
Proper Fractions,
Improper Fractions
Mixed Fractions.
1. Proper Fraction
A proper fraction is one in which the numerator (number of equal parts counted) is less than the denominator (total number of parts). These fractions are all less than on the number line.
Proper Fraction
The above pizza example, with each person receiving ⅜ th of the pizza, demonstrates a proper fraction.
2. Improper Fraction
An improper fraction occurs when the numerator (number of equal parts counted) is greater than the denominator (total number of parts). These fractions are greater than one and lie on the number line beyond one. When more than one thing is divided into equal halves, they come into play. The number of equal parts is represented by the denominator. The numerator represents the number of available parts.
For example, there are a total of 8 slices in each. One has 8 slices left, and the other has only 6 slices. So, the fraction representing;
Improper Fraction
Improper Fraction with 6 Parts
Addition of both pizza’s parts and whole = $1+\dfrac{6}{8}=\dfrac{14}{8}$
3. Mixed Fraction
As the name suggests, it combines a whole and a 'part.' By dividing the numerator by the denominator and obtaining the quotient and remainder, an improper fraction can be stated as a mixed fraction.
For example: $2 \dfrac{4}{6}$
4. Unlike Fractions
Fractions with different denominators are called unlike fractions. Here the denominators of fractions have different values.
So, it can also be defined as fractions having the same numerator and different denominators are known as unlike fractions.
For example: $\dfrac{4}{7}, \dfrac{4}{5}, \dfrac{4}{11}, \dfrac{4}{13}, \dfrac{4}{15}$
5. Like Fractions
Fractions with same denominator and different numerators are known as like fractions.
For example: $\dfrac{7}{8}, \dfrac{12}{8}, \dfrac{15}{8}, \dfrac{9}{8}, \dfrac{23}{8}$
6. Unit Fractions or Unique Fractions
Fractions that have 1 as a numerator are known as unit fractions or unique fractions.
For Examples: $\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}$
7. Equivalent Fractions
Equivalent fractions are fractions that have the same value when simplified.
For example: $\dfrac{1}{2} \text { and } \dfrac{50}{100}$ are equivalent to 0.5. As a result, these are comparable fractions.
Summary
This article discusses that a fraction is a portion of a complete part of the object. The fraction shows how many parts you have of anything when divided into several pieces. It is expressed as the number of equal parts counted (numerator) divided by the total number of parts (denominator). There are 7 kinds of fractions; Proper Fractions, Improper Fractions, Mixed Fractions, Like Fractions, Unit Fractions, Equivalent Fractions and Same Numerator Fractions. If you enjoyed reading this and want to learn more about fractions, visit our website.
FAQs on Types of Fractions in Maths: Explained with Examples
1. What is a fraction and why is it important in Maths?
A fraction represents a part of a whole or, more generally, any number of equal parts. It is written as a numerator (the top number) over a denominator (the bottom number). Fractions are fundamentally important because they allow us to express and work with values that are not whole numbers, which is crucial for precision in measurements, dividing quantities, and understanding ratios and proportions in everyday life and advanced mathematics.
2. What are the main types of fractions? Explain with examples.
The main types of fractions a student learns as per the NCERT syllabus are:
Proper Fractions: The numerator is smaller than the denominator. Example: 3/5, where the value is less than one.
Improper Fractions: The numerator is greater than or equal to the denominator. Example: 7/4, where the value is one or more.
Mixed Fractions: A whole number combined with a proper fraction. Example: 2 ¾, which is the same as 11/4.
Like and Unlike Fractions: Like fractions have the same denominator (e.g., 1/8 and 5/8), while unlike fractions have different denominators (e.g., 1/3 and 2/5).
Equivalent Fractions: Fractions that represent the same value. Example: 1/2 is equivalent to 2/4.
3. What is the key difference between a proper and an improper fraction?
The key difference lies in their value relative to 1. A proper fraction always represents a quantity less than one whole because its numerator is smaller than its denominator (e.g., 4/9). In contrast, an improper fraction represents a quantity equal to or greater than one whole because its numerator is equal to or larger than its denominator (e.g., 9/4).
4. How is a mixed fraction related to an improper fraction?
A mixed fraction and an improper fraction are two different ways to represent the same number greater than 1. An improper fraction like 11/4 can be converted into a mixed fraction by dividing the numerator (11) by the denominator (4). The result is a quotient of 2 (the whole number) and a remainder of 3 (the new numerator), giving the mixed fraction 2 ¾. They are simply different notations for the same value.
5. What is the importance of identifying like and unlike fractions?
Identifying fractions as 'like' or 'unlike' is critical for performing addition and subtraction. Like fractions (e.g., 3/8 and 2/8) have the same denominator, meaning their parts are of the same size, so their numerators can be added or subtracted directly. For unlike fractions (e.g., 1/2 and 1/3), you must first convert them into equivalent fractions with a common denominator before you can add or subtract them accurately.
6. How can you tell if two fractions are equivalent without simplifying them?
You can determine if two fractions are equivalent by using the cross-multiplication method. For two fractions, say a/b and c/d, you multiply the numerator of the first fraction by the denominator of the second (a × d) and compare it with the product of the second fraction's numerator and the first's denominator (c × b). If the products are equal (a × d = c × b), the fractions are equivalent.
7. How are fractions used in real-life situations beyond the classroom?
Fractions are essential in many real-world scenarios. Some common examples include:
Cooking and Baking: Recipes often call for fractional amounts like ½ cup of sugar or ¾ teaspoon of salt.
Shopping: Discounts are frequently shown as fractions, such as '1/3 off the original price'.
Telling Time: We use fractions to describe parts of an hour, like a 'quarter past' (¼) or 'half past' (½).
Construction and Crafting: Measurements often rely on fractions of an inch or a foot for precision.
8. Why can the denominator of a fraction never be zero?
The denominator of a fraction tells us into how many equal parts a whole has been divided. Conceptually, it is impossible to divide something into zero equal parts. In mathematics, division by zero is undefined because it does not have a meaningful result. Therefore, a fraction with a denominator of zero is not a valid number.
9. Why is it necessary to find a common denominator when adding or subtracting unlike fractions?
When fractions are unlike, they represent parts of different sizes (e.g., halves and thirds). You cannot meaningfully add or subtract parts of different sizes. Finding a common denominator is the process of converting these fractions into equivalent fractions where the parts are all the same size. Only then can you accurately combine (add) or take away (subtract) the numerators, as you are now working with a uniform unit.
10. How do you simplify a fraction to its lowest terms?
To simplify a fraction, you must divide both the numerator and the denominator by their Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF). For example, to simplify the fraction 24/36, the GCD of 24 and 36 is 12. Dividing the numerator (24 ÷ 12 = 2) and the denominator (36 ÷ 12 = 3) gives the simplified fraction 2/3.
