Mathematics Holiday Homework Project
Topic: Rational Numbers
Submitted by:
Name: [Your Name]
Class: VIII
Section: [Your Section]
Roll No.: 5
Session: 2024-25
Submitted to:
Teacher's Name: [Your Teacher's Name]
School Name:
[Your School's Name]
Cover Page
"Rational Numbers are present in every aspect of life —
From cutting cakes equally to measuring distances accurately,
From handling money to reading the time on a clock.
They simplify our world in a logical and systematic way."
Table of Contents
S.No Content Page No.
1 Introduction to Rational Numbers 1
2 History of Rational Numbers 2
3 Terminology and Symbols Used 3
4 Explanation of Rational Numbers 4
5 Game or Puzzle Related to the Topic 5
Mathematical Problems with Solutions
6 6
(2)
7 Real Life Applications (with Pictures) 7
8 Conclusion 8
1. Introduction of the Topic
Rational numbers are those numbers that can be expressed in the form p/q, where p and q are integers and q ≠ 0 .
These numbers are widely used in daily life — while sharing, measuring, calculating or trading.
Examples of Rational Numbers: 2/3, -4/5, 0, 5, 8/1
Rational numbers include positive numbers, negative numbers, zero, fractions, and terminating decimals.
2. History of Rational Numbers
The concept of Rational Numbers started in ancient times when Egyptians and Babylonians used fractions in daily trade and land measurement.
The term ‘Rational’ comes from the Latin word ‘Ratio’, meaning relation or comparison.
Greek Mathematicians, especially Pythagoras, used ratios to explain harmony in music and nature.
In 17th-century Europe, Rational Numbers became part of the modern number system.
Rational Numbers have played a key role in mathematics development worldwide.
3. Terminology and Symbols Used
Rational Numbers (Q): Represented by the letter Q.
Numerator (p): The top value in the fraction.
Denominator (q): The bottom value in the fraction (cannot be zero).
Equivalent Rational Numbers: Different fractions having the same value.
Example:
1/2 = 2/4 = 4/8
4. Explanation of the Topic
✔ Definition:
A Rational Number is any number that can be written in the form p/q, where p and q are integers and q ≠ 0 .
✔ Types of Rational Numbers:
1. Positive Rational Numbers: Both numerator and denominator have the same sign.
2. Negative Rational Numbers: Numerator and denominator have opposite signs.
3. Zero: It is also a Rational Number as it can be written as 0/q (q ≠ 0).
✔ Properties:
Closure Property: Addition, subtraction, multiplication, and division (except by zero) of two rational numbers is also rational.
Commutative Property: Addition and multiplication are commutative.
Associative Property: Addition and multiplication are associative.
Distributive Property: Multiplication is distributive over addition/subtraction.
5. Game or Puzzle Related to the Topic
Find the Missing Number Puzzle:
1. ? / 5 = 2 / 5 → ? = 2
2. -3 / ? = -3 / 7 → ? = 7
3. 4 / ? = 12 / 9 → ? = 3
6. Mathematical Problems with Solutions (Only 2)
Problem 1:
Find the sum of 3/8 and 5/12.
Solution:
LCM of 8 and 12 = 24
3/8 = 9/24
5/12 = 10/24
Sum = 9/24 + 10/24 = 19/24
✔ Answer: 19/24
Problem 2:
Multiply: (-2/3) × (3/4)
Solution:
(-2/3) × (3/4) = -6/12 = -1/2
✔ Answer: -1/2
7. Real Life Applications
Cooking: Measuring 1/2 cup of milk or 1/4 teaspoon of salt.
Construction: Cutting a wooden plank into 3/5 meter pieces.
Finance: Expressing ₹2.50 as 5/2 rupees.
Time Measurement: 15 minutes as 1/4 hour.
8. Conclusion
Rational Numbers are an essential part of mathematics and daily life.
They help us solve real problems related to division, measurement, calculation, and proportion.
A proper understanding of Rational Numbers builds the foundation for higher mathematical studies.
