Important Fractions Questions

Solving fraction questions is important to get a strong hold of this topic. As fractions are a foundational maths topic, it is crucial for kids to clear doubts and build conceptual fluency by practising a lot of fraction questions. Fractions are not only used in mathematics; they hold significance in real life too. Whether you’re sharing a pizza or a bar of chocolate, fractions are used everywhere. Let’s learn in detail about fractions and their types to understand how to perform arithmetic operations on them. 

Table of Contents

• Definition
• Parts of a Fraction
• Types of Fractions
• Arithmetic Operations on Fractions
• Sample Fractions Questions
• Frequently Asked Questions
• Conclusion

Definition

Parts of a Fraction

A fraction represents a part of a whole and is written as a/b, where a and b are the numerator and denominator. Both a and b are whole numbers, and b ≠ 0. For example, 3/4, 1¾, etc.

Numerator of a Fraction: The number placed at the top of a fraction '/' is called a numerator.

Denominator of a Fraction: The number placed at the bottom of a fraction '/' is called a numerator.

Types of Fractions

Understanding different types of fractions makes it easier to solve fractions questions correctly:

I. Proper Fractions: A fraction in which the numerator is less than the denominator is called a proper fraction. For example, ⅗ and 4/9

II. Improper Fractions: A fraction in which the numerator is greater than or equal to the denominator. For example, 7/4.

III. Mixed Fractions: When a whole number is combined with a proper fraction, it is called a mixed fraction. For example, 1¾.

IV. Like & Unlike Fractions: Like fractions are fractions that have the same denominator. For example, ⅖ and ⅗ are like fractions. Fractions with different denominators are called unlike fractions. For example, ¼ and ⅔ are unlike fractions. 

V. Inverse Fractions: An inverse fraction is a fraction that you get when you flip the numerator and denominator of a fraction. The reciprocal of a fraction is important for multiplication and division of fractions.

Arithmetic Operations on Fractions

Fraction questions often involve addition, subtraction, multiplication, and division. Here's how to perform them:

Addition & Subtraction of Fractions

Step 1: The first step in addition of fractions is to make the denominators the same. For both addition and subtraction, if the denominators are different, calculate the least common denominator. For example, to add ¼ & ⅙, the LCD is 12, so convert both fractions, i.e., ¼ = 3/12 and ⅙ = 2/12. ​

Step 2: Add or subtract the numerators. 

Now that the denominators are the same, simply add the numerators: 3/12 + 2/12 = 5/12.

Step 3: Simplify the result if needed.
 

Multiplication of Fractions

To multiply fractions, first multiply the numerators together and then multiply the denominators together. After getting the result, simplify it further and get the final answer.

For example, Multiply ¾ with ⅔ 

First, multiply 3 & 2 to get the numerator as 6 and then 4 & 3 to get the denominator as 12. At the end, simplify 6/12 to ½ 

Sample Fractions Questions 

A step-by-step guide to solve some sample fraction questions will help you grasp the concepts easily. 

1. Add the fractions 5/6 and 7/6.

 Since the denominator is the same, we can add numerators and simplify it further. 

 5/6 + 7/6 = (5 + 7)/6 = 12/6 = 2

2. Multiply the following fractions.

 (i) (⅖) × 5 ¼

(ii) 2 ⅗ × 3

Solution:

 (i) Multiply (⅖) × 5 ¼

 Here, 5 ¼ is a mixed fraction.

Let us convert this mixed fraction into an improper fraction.

5 ¼ = [(5 × 4) + 1]/4 = 21/4

Thus, (⅖) × 5 ¼ = (⅖) × (21/4) = 21/10

(ii) Multiply 2 ⅗ × 3

 Here, 5 ¼ is a mixed fraction.

 Let us convert this mixed fraction into an improper fraction.

 2 ⅗ = [(5 x 2) + 3]/5 = 13/5

Thus, (13/5) x 3 = 39/5

3. Divide 3/10 by (1/4 of 3/5).

Solution:

1/4 of 3/5 = (1/4) × (3/5) = 3/(4 × 5) = 3/20 

3/10 ÷ (1/4 of 3/5)

 = 3/10 ÷ 3/20

 = (3/10) × (20/3)

= 2

4. Ankit can finish a piece of work in 5 hours. What part of the work can he finish in 1 hour, 2 hours and by 4 hours?

Solution:

Let's denote the whole work done by Ankit as 'n'

So, the total amount of work Ankit completed in 5 hours = n

The work completed by Ankit in 1 hour = n/5

Similarly, the work complete by Ankit in 2 hours =  2 x (n/5) = 2n/5

And, the work complete by Ankit in 4 hours = 4 x (n/5) = 4n/5

Therefore, Ankit can complete 1/5 part of his work in 1 hour, 2/5 of his work in 2 hours, and 4/5 of his work in 4 hours.

Frequently Asked Questions

Q1: Why do we need to learn fractions?

Fractions are an important maths topic with many applications in real life. They form the foundation for learning advanced math skills. Some of the daily activities where we use the concept of fractions are cooking, measurements, dividing bills, and more.

Q2: How do I convert a mixed number to a fraction?

Multiply the whole number by the denominator, add the numerator, and place it over the original denominator.​

Q3: Can the denominator be zero?

No. A denominator can never be zero because division by zero is undefined.

Q4: How do I simplify a fraction?

To simplify a fraction, divide both the numerator and denominator by their highest common factor (HCF).

Conclusion 

Fractions are a fundamental part of mathematics and everyday life. They represent parts of a whole, ratios, and divisions, and they are essential in many fields, from cooking and construction to science, finance, and technology. By learning with Orchid's math concept pages, you can easily gain an in-depth understanding of important math topics.