🔢 Rational Numbers Explorer ➗

Rational Numbers for Class 8 Online Practice Worksheet

Class 8 Rational Numbers Worksheet Free Online: Build strong Class 8 Mathematics skills with DigiSadhan's interactive Rational Numbers Online Practice Worksheet. This free learning tool provides repeated practice with positive and negative rational numbers, addition, subtraction, multiplication, division, comparison, ordering, reciprocals and important properties. Generate up to 1,000 unique questions and use Shuffle Whole Worksheet to create a fresh practice set whenever you need one. Select Foundation, Class 8 Core, Challenge or Mixed level, then choose a specific topic or mixed revision. Every question includes an easy answer textbox and Check Answer button. A correct response changes the textbox to green and gives a positive animation and sound; an incorrect response changes it to red and provides a retry animation and sound. The Show Answer button remains unavailable until the question has been checked, while the complete answer key stays locked until the test is completed. A live progress bar, score, checked-question count and percentage make progress easy to understand. Students can choose no timer or a 5, 10, 15, 30 or 60-minute timed session. At the end, the final score and performance message are displayed, and the worksheet can be downloaded as a printable PDF. The responsive mobile-first design works on smartphones, tablets, laptops and classroom computers. Visual fraction cards and number-line style graphics help students understand signs, equivalent fractions and rational-number operations. The tool is useful for homework, classroom revision, tuition, self-study, worksheet practice, test preparation and regular Class 8 Maths revision.

Complete Class 8 Rational Numbers Practice Guide

What Is a Rational Number?

A rational number is any number that can be expressed in the form p/q, where p and q are integers and q is not zero. Rational numbers include positive numbers, negative numbers and zero. Examples include 3/5, −7/4, 8/1 and 0. A decimal that terminates or repeats can also be represented as a rational number.

Standard Form

A rational number is in standard form when the numerator and denominator have no common factor other than 1 and the denominator is positive. For example, 12/18 becomes 2/3 after dividing numerator and denominator by their greatest common factor, 6.

Equivalent Rational Numbers

Multiplying or dividing both the numerator and denominator of a rational number by the same non-zero integer gives an equivalent rational number. For example, 2/3 = 4/6 = 6/9. Equivalent fractions represent the same value even though their numerator and denominator look different.

Addition of Rational Numbers

To add rational numbers with the same denominator, add their numerators and keep the denominator unchanged. For different denominators, find a common denominator, usually by using the LCM of the denominators. Convert both numbers to equivalent fractions and then add. Pay close attention to signs when adding positive and negative rational numbers.

Subtraction of Rational Numbers

Subtraction can be changed into addition of the additive inverse. This is especially helpful with negative rational numbers. For example, a − b is the same as a + (−b). After changing the operation, use the rules for addition and simplify the final fraction.

Multiplication of Rational Numbers

To multiply rational numbers, multiply the numerators together and the denominators together. Before multiplying, common factors can be cancelled across a numerator and denominator to make the calculation easier. The sign follows the multiplication sign rule: positive × positive is positive, negative × negative is positive, and positive × negative is negative.

Division of Rational Numbers

To divide one rational number by another, multiply the first number by the reciprocal of the second number. The divisor cannot be zero because division by zero is undefined. When taking a reciprocal, interchange the numerator and denominator, while keeping the sign unchanged.

Reciprocal

The reciprocal of a non-zero rational number is obtained by interchanging its numerator and denominator. The reciprocal of 5/7 is 7/5, while the reciprocal of −3/8 is −8/3. Zero has no reciprocal because there is no number that can be multiplied by zero to produce 1.

Comparing Rational Numbers

Rational numbers can be compared using a common denominator, cross multiplication when denominators are positive, decimal representations, or a number line. For example, to compare 3/4 and 5/8, convert 3/4 to 6/8. Since 6/8 is greater than 5/8, 3/4 is greater than 5/8.

Properties of Rational Numbers

Rational numbers are closed under addition, subtraction and multiplication. They are also closed under division provided the divisor is not zero. Addition and multiplication are commutative, meaning the order can be changed without changing the result. Subtraction and division are not commutative.

Associative and Distributive Properties

Addition and multiplication are associative: (a + b) + c = a + (b + c), and (a × b) × c = a × (b × c). Subtraction and division are not associative. Multiplication is distributive over addition and subtraction: a(b + c) = ab + ac and a(b − c) = ab − ac.

Rational Numbers on a Number Line

Positive rational numbers lie to the right of zero and negative rational numbers lie to the left. The farther a number is to the right, the greater it is. The farther a negative number is to the left, the smaller it is. Number-line thinking is useful for comparing rational numbers and understanding signs.

Common Mistakes to Avoid

• Forgetting that the denominator can never be zero.
• Adding denominators when adding fractions.
• Changing the sign incorrectly when subtracting a negative number.
• Forgetting to take the reciprocal when dividing.
• Leaving a fraction unsimplified when simplest form is required.
• Assuming subtraction or division is commutative.
• Using a reciprocal for zero.
• Comparing numerators without considering the denominators.

Best Strategy for Class 8 Rational Number Questions

1. Identify the operation and signs first.
2. Write each rational number clearly as a fraction.
3. For addition or subtraction, find a common denominator.
4. For multiplication, cancel common factors before multiplying when useful.
5. For division, multiply by the reciprocal of the divisor.
6. Check the sign of the answer.
7. Reduce the final fraction to standard form.
8. Estimate the result to catch calculation errors.

Quick Rational Numbers Formula Sheet

Regular practice makes rational-number calculations faster and more reliable. Use the shuffle feature to generate new question sets, move from Foundation to Core and Challenge levels as your confidence improves, and use the timer for exam-style revision. The most effective habit is to show each step: simplify fractions, track negative signs, identify the correct operation and check the final result. With repeated practice, Class 8 students can confidently add, subtract, multiply and divide rational numbers and explain the properties that make these operations work.