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MathematicsClass 8Rational Numbers

Rational Numbers | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 3 min read

Rational Numbers – this guide gives you a concise, exam-ready overview of Rational Numbers from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Operations on Rational Numbers

Arithmetic operations on rational numbers include addition, subtraction, multiplication, and division. These operations follow specific rules to ensure the result is also a rational number. Addition and subtraction require a common denominator. To add or subtract a/b and c/d, convert both to equivalent fractions with denominator bd: a/b + c/d = (ad + bc)/bd and a/b - c/d = (ad - bc)/bd. Multiplication is straightforward: multiply numerators and denominators separately: (a/b) × (c/d) = (ac)/(bd). Division involves multiplying by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c), provided c ≠ 0. The operations obey the properties of rational numbers such as closure, commutativity, associativity, and distributivity. When performing these operations, it is important to simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). Also, when dealing with negative rational numbers, the sign rules apply: the product or quotient of two rational numbers with the same sign is positive; with different signs, it is negative. Mastery of these operations is essential for solving algebraic expressions and real-life problems involving rational quantities.

📊 Diagram: The textbook uses fraction bars and number line illustrations to demonstrate addition and subtraction of rational numbers, and multiplication tables to show multiplication and division.

🧪 Activity: Students perform addition, subtraction, multiplication, and division of given pairs of rational numbers and simplify the results.

🔗 Connection: This section leads to the next section on word problems involving rational numbers, applying these operations.

Frequently asked questions

1. Name the property under multiplication used in each of the following. (i) \(\frac{-4}{5} \times 1 = 1 \times \frac{-4}{5} = -\frac{4}{5}\) (ii) \(-\frac{13}{17} \times \frac{-2}{7} = \frac{-2}{7} \times \frac{-13}{17}\) (iii) \(\frac{-19}{29} \times \frac{29}{-19} = 1\)

Solution: (i) The property used here is the Multiplicative Identity Property, which states that any number multiplied by 1 remains unchanged.

(ii) The property used here is the Commutative Property of Multiplication, which states that changing the order of factors does not change the product.

(iii) The property used here is the Multiplicative Inverse Property, which states that a number multiplied by its reciprocal equals 1.

2. Tell what property allows you to compute \(\frac{1}{3} \times \left(6 \times \frac{4}{3}\right)\) as \(\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\) .

Solution: The property used here is the Associative Property of Multiplication. It states that when three or more numbers are multiplied, the product is the same regardless of how the numbers are grouped.

So, \(\frac{1}{3} \times \left(6 \times \frac{4}{3}\right) = \left(\frac{1}{3} \times 6\right) \times \frac{4}{3}\).

3. The product of two rational numbers is always a

Solution: The product of two rational numbers is always a rational number.

Explanation: Rational numbers are closed under multiplication, meaning the product of any two rational numbers is also a rational number.

Which of the following numbers is a rational number?

\frac{3}{4}

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