103 LearnersLast updated on July 4th, 2025
Fractions
A fraction is a mathematical value representing a part of a whole, such as a pizza slice from a full pizza. In this topic, we will be learning about fractions, their types, and properties.
What are Fractions?
Fractions represent a part of a whole. They are usually expressed in this form: ab, where ‘a’ and ‘b’ are called the numerator and denominator, respectively. Out of the whole, numerator represents a part of the whole while, denominator denotes the whole number. Together, they tell us how much of something we have.
A fraction represents how to divide a whole into equal parts. For example, if a circle is divided into 12 equal parts and one piece of the circle is represented as 1/12, it is read as one-twelfth.
What are the Types of Fractions?
Fractions are categorized based on the relationship between the numerator and denominator. Let's take a look at the types of fractions:
- Proper Fraction
- Improper Fraction
- Unit Fraction
- Mixed Fraction
- Equivalent Fraction
- Like Fraction
- Unlike Fraction
Proper Fractions: In proper fractions, the numerator is less than the denominator. For instance, 2/8, 6/15, 7/9, …
Improper Fractions: The numerator is greater than or equal to the denominator
For instance, 8/2, 5/3, 15/6, …
Unit Fractions: In a fraction, where the numerator is always 1, it is called a unit fraction. Unit fractions have a numerator of 1 and are always proper fractions (e.g., 1/5, 1/9, 1/12).
Mixed Fractions: A mixed fraction consists of a whole number and a proper fraction. For example, 614, here, 6 is the whole number and ¼ is the proper fraction.
Equivalent Fractions: Equivalent fractions are two or more fractions with different numbers but the same value. For example, 1/2 = 2/4 = 3/6. Here, 1/2, 2/4, and 3/6 share the same value because they all represent half of a whole. Equivalent fractions are resulted by multiplying or dividing the numerator and denominator by the same number (e.g., 1/2 × 2/2 = 2/4).
Like Fractions: The fractions with the same denominators are called fractions. For example, 5/17, 6/17, 9/17,…
Unlike Fractions: Fractions with different denominators. E.g., 5/12, 6/18, 9/11, …
How to Represent Fractions on a Number Line
The visual representation of numbers using a horizontal straight line is the number line. A fraction on a number line helps students to understand how the number is divided into parts between the two whole numbers. The denominator represents the number of parts the number line will be divided into.
What are the Properties of Fractions
Fractions share properties with other numbers. Here, we are going to discuss some of the properties of fractions.
- Commutative property: When multiplying and adding fractions, the order of the values does not affect the result. That is a/b + c/d = c/d + a/b and a/b × c/d = c/d ×a/b.
- Associative property: The way of grouping the fractions in addition and multiplication doesn’t affect the result. For example, (a/b + c/d) + e/f = a/b + (c/d + e/f) and (a/b × c/d) × e/f = a/b × (c/d × e/f)
- Identity property: The product of a fraction multiplied by 1 is the fraction itself. For example, a/b × 1 = a/b. Adding 0 to a fraction has no effect on the final outcome. So, a/b + 0 = a/b
- Multiplicative inverse: Multiplying a fraction by its reciprocal yields 1, that is (a/b) × (b/a) = 1
- Distributive property: The product of multiplying a fraction by the sum of two fractions is equal to the sum of the product multiplied by each addend separately. That is a/b × (c/d + e/f) = a/b × c/d + a/b × e/f
Real-world Applications of Fractions
Fractions play an important role in our everyday lives. In fact, we use them often even without realizing it. Fractions are used daily in tasks like cooking, measuring, and calculating discounts.
Take a look at the below-mentioned scenarios where fractions are used:
- In cooking and baking, we use fractions to adjust the ingredients that are added in the right proportions.
- Since fractions help us express values accurately, we use them to measure land areas and distances where precise measurements are required.
- We also use fractions to calculate the discounts and interest rates.
- To express the score for students, fractions are used.
Common Mistakes and How to Avoid Them in Fractions
When learning fractions and doing calculations, students often make errors when working with fractions. This section covers common mistakes and how to avoid them when working on fractions.
Mistake 1
Adding and subtracting unlike fractions without converting
Adding or subtracting unlike fractions without converting them into like fractions is a common mistake. Not converting unlike fractions before addition or subtraction will lead to wrong answers. For example, let’s say we want to add 1/4 + 1/3. Adding them without converting yields 2/7, which is wrong. So, 1/4 can be converted into 3/12 and 1/3 can be written as 4/12. Now that we have a common denominator (12), we can add them up. Therefore, 3/12 + 4/12 = 7/12.
Mistake 2
Dividing fractions without flipping the second fraction
When dividing fractions, students tend to forget to take the reciprocal of the divisor. E.g., in 1/2 ÷ 3/4, they might incorrectly express it as 1/2 × 3/4 instead of the correct 1/2 × 4/3. Always remember that we should divide a fraction only after multiplying by its reciprocal. So, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
Mistake 3
Not simplifying the fraction
Students forget to reduce fractions into simple terms correctly. Always divide the numerator and denominator by their greatest common factor (e.g., 4/6 = 2/3).
Mistake 4
Errors when converting mixed fractions
In calculating mixed fractions, mixing up the multiplication or addition can lead to errors. So, it is important to understand the conversion process. For instance, when converting 614, that is 6 × 4 + 1 = 25, so that can be converted to 25/4.
Mistake 5
Cross multiplication errors
Students may misuse cross multiplication when adding or subtracting fractions. To add or subtract, find a common denominator (e.g., LCM of 4 and 5 is 20).
Solved Examples of Fractions
Problem 1
A farmer planted three-fifths of his land with wheat and two-sevenths with corn. What fraction of his land is planted with crops?
The fraction of his land planted with crops is 31/35
Explanation
3/5 of the farmer’s land is used to grow wheat, while 2/7 of his land is dedicated to corn.
The fraction of his land planted with wheat and corn is 3/5 + 2/7
Since the fractions have different denominators, we should convert them before adding. To convert the fractions, let us first find the least common denominator (LCD).
The LCD of 5 and 7 is 35.
Now, let us convert 3/5 such that it has 35 as the denominator:
3/5 = (3 × 7) / (5 × 7) = 21/35
Converting 2/7, we get, 2/7 = (2 × 5) / (7 × 5) = 10/35
Thus, 3/5 + 2/7 = 21/35 + 10/35 = 31/35.
Problem 2
A recipe requires three-fourths of a cup of sugar. If you want to make five-sixths of the recipe, how much sugar do you need?
The amount of sugar needed is ⅝ cups.
Explanation
The amount of sugar needed = 3/4
So, to make 5/6 of the recipe, the sugar required = (¾) × (⅚)
= 15/24 = 5/8
Problem 3
A rope is four-ninths of a meter long. It is cut into pieces, each measuring two-thirds of a meter. How many pieces can be made?
The number of pieces that can be made is 2/3
Explanation
To determine how many pieces you can make, divide the total length of the rope by the length of one piece = (4/9) ÷ (2/3)
= (4/9) × (3/2)
= 12/18 = 2/3
Problem 4
Lisa bought 2 whole pizzas and three-fifths of another pizza. Express the total as an improper fraction.
So, it can be expressed as 13/5
Explanation
The pizza Lisa bought = 235
It can be converted to improper fraction as 2 × 5 + 3 = 13
That is 13/5
Problem 5
A group of students collected seventeen-fourths of a kilogram of rice. Express this as a mixed fraction.
The amount of rice collected by the students is 414 kgs
Explanation
The amount of rice collected by the students = 17/4
To express 17/4 as a mixed fraction, we divide 17 by 4, with the remainder of 1
So, it can be expressed as 414.
FAQs on Fractions
1.What is a fraction?
2.What are the types of fractions?
3.What is 3.3 as a fraction in the simplest form?
4.What is 1/4 × 1/4?
5.What is 1.25 as a fraction?
6.How can children in Canada use numbers in everyday life to understand Fractions?
7.What are some fun ways kids in Canada can practice Fractions with numbers?
8.What role do numbers and Fractions play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Fractions skills?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
