Rational Numbers Overview

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Questions and Answers

What is the additive inverse of a rational number 'a/b'?

  • -b/a
  • -a/b (correct)
  • a/b
  • b/a

What will be the result of adding 0 to any rational number 'x'?

  • 1
  • -x
  • x (correct)
  • 0

Identify the multiplicative inverse of the rational number 3/4.

  • 3/4
  • 4/3 (correct)
  • 12
  • 1/12

Which of the following statements about the number 1 is true in the context of multiplication?

<p>It is the multiplicative identity. (D)</p> Signup and view all the answers

What type of number is found between any two rational numbers?

<p>Infinitely many rational numbers (C)</p> Signup and view all the answers

Which of the following represents a positive rational number?

<p>$\frac{2}{3}$ (A), $\frac{-4}{-5}$ (C)</p> Signup and view all the answers

What is the closure property in the context of rational numbers?

<p>The operations yield a rational number. (B)</p> Signup and view all the answers

Which statement correctly describes the commutative property?

<p>$a + b = b + a$ and $a \times b = b \times a$ (B)</p> Signup and view all the answers

Which of the following is an example of a zero rational number?

<p>$\frac{0}{3}$ (A)</p> Signup and view all the answers

Which property states that the order of addition does not affect the outcome?

<p>Commutative Property (D)</p> Signup and view all the answers

What is the form of a rational number?

<p>$\frac{p}{q}$ where q &gt; 0. (C)</p> Signup and view all the answers

Which of the following is an example of the distributive property?

<p>$a \times (b + c) = ab + ac$ (B)</p> Signup and view all the answers

Which of the following statements regarding rational numbers is true?

<p>Rational numbers can be represented on a number line. (C)</p> Signup and view all the answers

Flashcards

Rational Number

A number that can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.

Additive Identity (Zero)

The sum of any rational number and zero is the rational number itself.

Multiplicative Identity (One)

The product of any rational number and one is the rational number itself.

Additive Inverse

The additive inverse of a rational number is the same number with the opposite sign.

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Multiplicative Inverse (Reciprocal)

The multiplicative inverse of a rational number is its reciprocal, which is obtained by flipping the numerator and denominator.

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Positive Rational Number

A rational number where the numerator and denominator have the same sign (both positive or both negative).

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Negative Rational Number

A rational number where the numerator and denominator have opposite signs (one positive and one negative).

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Zero Rational Number

A rational number where the numerator is zero and the denominator is any non-zero integer.

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Closure Property of Rational Numbers

In an operation (like addition, subtraction, or multiplication) on two rational numbers, the result is always a rational number.

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Commutative Property of Rational Numbers

The order of rational numbers in addition or multiplication doesn't affect the answer.

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Associative Property of Rational Numbers

The way numbers are grouped in addition or multiplication doesn't affect the answer.

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Distributive Property of Rational Numbers

A property that shows how multiplication distributes over addition or subtraction. For example, a(b + c) = ab + ac.

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Study Notes

Rational Numbers

  • Rational numbers are numbers in the form p/q, where q > 0. They are denoted by Q.
  • A rational number is in standard form if the numerator and denominator are coprime (share no common factors other than 1) and the denominator is positive.

Types of Rational Numbers

  • Positive rational numbers: Both the numerator and denominator are either positive or negative. Examples: 2/3, -7/-8
  • Negative rational numbers: The numerator and denominator have opposite signs. Examples: 2/-7, -3/8
  • Zero rational numbers: The numerator is zero. Example: 0/8

Properties of Rational Numbers

  • Closure Property: Adding, subtracting, or multiplying any two rational numbers always results in another rational number.
  • Commutative Property: The order of adding or multiplying rational numbers does not change the answer. For example: 2/3 + 4/5 = 4/5 + 2/3
  • Associative Property: The grouping of rational numbers when adding or multiplying does not change the answer.
  • Distributive Property: Multiplying a rational number by the sum (or difference) of two rational numbers is the same as multiplying the rational number by each number in the sum (or difference) and then adding (or subtracting) the products. For example, a(b + c) = ab + ac.
  • Additive Identity: Adding zero to any rational number results in the original rational number.
  • Multiplicative Identity: Multiplying any rational number by one results in the original rational number.
  • Additive Inverse: The additive inverse of a rational number is the opposite (negative) of the number. When you add a number and its additive inverse, the result is zero.
  • Multiplicative Inverse (Reciprocal): The multiplicative inverse (or reciprocal) of a rational number is the number flipped upside down. When you multiply a number by its multiplicative inverse, the result is one. For a rational number a/b, its multiplicative inverse is b/a.

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CBSE Class 8 Maths Notes on Rational Numbers PDF

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