{"id":3209,"date":"2026-06-03T12:10:27","date_gmt":"2026-06-03T06:40:27","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=3209"},"modified":"2026-06-04T11:46:01","modified_gmt":"2026-06-04T06:16:01","slug":"ncert-class-9-maths-exercise-3-3-solutions-rational-numbers","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-3-3-solutions-rational-numbers\/","title":{"rendered":"NCERT Class 9 Maths Exercise 3.3 Solutions \u2013 Rational Numbers"},"content":{"rendered":"
\"image_print\"Print<\/span><\/a> 2<\/span><\/div>\n

Short Introduction<\/h1>\n\n\n\n

Exercise 3.3 focuses on the properties and operations of Rational Numbers. In this exercise, students learn how to verify equivalent rational numbers and perform addition, subtraction, multiplication, and division of fractions. Understanding these concepts is essential for mastering higher-level algebra and number systems.<\/p>\n\n\n\n

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Quick Information Box<\/h1>\n\n\n\n
Topic<\/th>Details<\/th><\/tr>
Chapter<\/td>The World of Numbers<\/td><\/tr>
Exercise<\/td>3.3<\/td><\/tr>
Class<\/td>Grade 9<\/td><\/tr>
Subject<\/td>Mathematics<\/td><\/tr>
Main Concepts<\/td>Rational Numbers, Equivalent Fractions, Arithmetic Operations<\/td><\/tr>
Difficulty Level<\/td>Easy to Moderate<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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Concepts Used (Topics Covered)<\/h1>\n\n\n\n

\u2714 Rational Numbers<\/p>\n\n\n\n

\u2714 Equivalent Fractions<\/p>\n\n\n\n

\u2714 Equality of Rational Numbers<\/p>\n\n\n\n

\u2714 Addition of Rational Numbers<\/p>\n\n\n\n

\u2714 Subtraction of Rational Numbers<\/p>\n\n\n\n

\u2714 Multiplication of Rational Numbers<\/p>\n\n\n\n

\u2714 Division of Rational Numbers<\/p>\n\n\n\n

\u2714 Lowest Common Multiple (LCM)<\/p>\n\n\n\n

\u2714 Simplification of Fractions<\/p>\n\n\n\n

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Important Formulas<\/h1>\n\n\n\n

1. Equality of Rational Numbers<\/h3>\n\n\n\n

Two rational numbers are equal if:<\/p>\n\n\n\n

a\/b = c\/d<\/p>\n\n\n\n

when<\/p>\n\n\n\n

ad = bc<\/p>\n\n\n\n

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2. Addition<\/h3>\n\n\n\n

a\/b + c\/d = (ad + bc)\/bd<\/p>\n\n\n\n

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3. Subtraction<\/h3>\n\n\n\n

a\/b \u2212 c\/d = (ad \u2212 bc)\/bd<\/p>\n\n\n\n

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4. Multiplication<\/h3>\n\n\n\n

a\/b \u00d7 c\/d = ac\/bd<\/p>\n\n\n\n

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5. Division<\/h3>\n\n\n\n

a\/b \u00f7 c\/d = a\/b \u00d7 d\/c<\/p>\n\n\n\n

(c \u2260 0)<\/p>\n\n\n\n

Exercise 3.3 Solutions<\/strong><\/p>\n\n\n\n

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Common Mistakes<\/h1>\n\n\n\n
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  1. Forgetting to simplify the final fraction to its lowest form.<\/li>\n\n\n\n
  2. Adding or subtracting numerators directly when denominators are different.<\/li>\n\n\n\n
  3. Multiplying fractions without reducing common factors first.<\/li>\n\n\n\n
  4. Dividing fractions without taking the reciprocal of the second fraction.<\/li>\n\n\n\n
  5. Ignoring negative signs while performing operations.<\/li>\n\n\n\n
  6. Using incorrect LCM while adding or subtracting rational numbers.<\/li>\n\n\n\n
  7. Cancelling terms across addition or subtraction signs, which is not allowed.<\/li>\n\n\n\n
  8. Making arithmetic errors while applying the distributive property.<\/li>\n\n\n\n
  9. Forgetting that a negative divided by a positive gives a negative result.<\/li>\n\n\n\n
  10. Not checking whether both sides are equal while proving identities.<\/li>\n<\/ol>\n\n\n\n
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    Exam Tips<\/h1>\n\n\n\n

    \u2705 Always write fractions in simplest form.<\/p>\n\n\n\n

    \u2705 While adding or subtracting fractions, first make denominators equal.<\/p>\n\n\n\n

    \u2705 Remember:<\/p>\n\n\n\n