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Mathematics Class 7 - Rational Numbers Notes

Comprehensive study notes for Class 7 - Rational Numbers olympiad preparation

Rational Numbers

Welcome to the chapter on Rational Numbers for Class 7. In this chapter, you will learn what rational numbers are, how to represent them, and how to perform operations with them. By the end of this chapter, you will be able to solve problems involving rational numbers confidently!

Introduction

Rational numbers are numbers that can be written as a fraction, where both the numerator and denominator are integers and the denominator is not zero. Rational numbers include positive numbers, negative numbers, and zero.

Definition of Rational Numbers

  • A rational number is a number that can be written as p/q, where p and q are integers and q ≠ 0.
  • Examples: 2/3, -5/7, 4/1, 0/9

Properties of Rational Numbers

  • Rational numbers can be positive, negative, or zero.
  • Every integer is a rational number (e.g., 5 = 5/1).
  • Rational numbers can be represented on a number line.

Equivalent Rational Numbers

Two rational numbers are equivalent if they represent the same value. You can get equivalent rational numbers by multiplying or dividing both numerator and denominator by the same non-zero integer.

  • Example: 2/3 = 4/6 = 6/9

Standard Form of Rational Numbers

A rational number is in standard form when the denominator is positive and the numerator and denominator have no common factors except 1.

  • Example: -6/8 can be written as -3/4 in standard form.

Operations on Rational Numbers

  • Addition: Find a common denominator, then add numerators.
  • Subtraction: Find a common denominator, then subtract numerators.
  • Multiplication: Multiply numerators and denominators.
  • Division: Multiply by the reciprocal of the divisor.

Example:
Addition: 1/2 + 1/3 = (3 + 2)/6 = 5/6
Multiplication: 2/5 × 3/4 = 6/20 = 3/10

Comparing Rational Numbers

To compare rational numbers, convert them to a common denominator and compare the numerators.

  • Example: 2/5 and 3/10 → 2/5 = 4/10, so 4/10 < 3/10

Fun Activity: Rational Number Line!

Draw a number line and mark rational numbers like -1/2, 0, 1/3, 2/3, 1. See how they are placed between integers!

Summary

  • Rational numbers can be written as fractions with integer numerator and denominator (denominator ≠ 0).
  • You can add, subtract, multiply, and divide rational numbers.
  • Rational numbers can be positive, negative, or zero.

Practice Questions

  1. Write two rational numbers between 0 and 1.
  2. Express 12 as a rational number.
  3. Add: 3/4 + 1/2
  4. Multiply: -2/3 × 3/5
  5. Compare: 5/8 and 3/4

Challenge Yourself

  • Write any three rational numbers with negative numerators.
  • Find the standard form of 18/24.

Did You Know?

  • All integers and fractions are rational numbers!
  • There are infinite rational numbers between any two numbers!

Glossary

  • Numerator: The top number in a fraction.
  • Denominator: The bottom number in a fraction.
  • Reciprocal: Flipping the numerator and denominator.
  • Standard Form: Fraction with no common factors except 1 and positive denominator.

Answers to Practice Questions

  1. 1/2, 3/4 (any two between 0 and 1)
  2. 12/1
  3. 3/4 + 1/2 = 3/4 + 2/4 = 5/4
  4. -2/3 × 3/5 = -6/15 = -2/5
  5. 5/8 < 3/4

Practice with rational numbers to become confident in solving math problems!

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