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NCERT Solutions for CBSE Class 6 Mathematics Chapter 7: Fractions

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CBSE Class 6 Mathematics Chapter 7 Fractions marks a pivotal transition in a student's mathematical journey from whole numbers to rational numbers. This chapter from the NCERT textbook 2024-25 edition systematically introduces fractions as parts of a whole, then progresses through like and unlike fractions, equivalent fractions, comparison techniques, all four arithmetic operations, visual representation on number lines, and finally decimal notation. Parents often notice this is where students either consolidate their numerical fluency or begin to struggle with abstract concepts. The NCERT solutions provided here follow the exact sequence and methodology prescribed by CBSE, ensuring students develop both procedural accuracy and conceptual clarity that will serve them through secondary school mathematics.

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Key takeaways

✓CBSE Class 6 Mathematics Chapter 7 Fractions covers six major topics: like and unlike fractions, equivalent fractions, comparing fractions, fraction operations, number line representation, and decimal conversion.
✓Mastering equivalent fractions in Class 6 Mathematics Chapter 7 is critical because the concept appears in 40% of fraction-related questions in CBSE assessments.
✓NCERT Class 6 Mathematics Chapter 7 dedicates substantial exercises to operations on fractions, with addition and subtraction forming the foundation for algebraic expressions in Class 7.
✓The chapter systematically builds from basic fraction identification to complex operations, following a spiral learning approach that CBSE recommends for concept retention.
✓Understanding fractions on a number line (covered in CBSE Class 6 Mathematics Chapter 7 Fractions) helps students visualize abstract numerical relationships and prepares them for coordinate geometry.
✓Decimal representation introduced in this chapter connects directly to percentage calculations in Chapter 8, making thorough practice essential.
✓Students who struggle with CBSE Class 6 Mathematics Chapter 7 Fractions often face difficulties in ratio, proportion, and percentage topics throughout Classes 7-10.

Understanding the Structure of CBSE Class 6 Mathematics Chapter 7 Fractions

The NCERT textbook organizes CBSE Class 6 Mathematics Chapter 7 Fractions into six progressive sections, each building upon the previous one. The chapter begins with a revision of what fractions represent (numerator and denominator), then introduces like fractions (same denominator) and unlike fractions (different denominators). Section 7.2 explores equivalent fractions through visual models and multiplication/division principles. Section 7.3 teaches systematic comparison of fractions using LCM and cross-multiplication methods. Section 7.4 forms the heart of the chapter with addition and subtraction of like and unlike fractions, while Section 7.5 extends to multiplication and division. Section 7.6 places fractions on number lines, helping students visualize magnitude and order. The final section bridges fractions to decimals, showing how 3/4 equals 0.75. This structure aligns perfectly with the CBSE's competency-based framework, which emphasizes understanding (20%), application (40%), and problem-solving (40%).

Exercise 7.1 covers identification and classification of like and unlike fractions with 15 questions
Exercise 7.2 focuses on finding and verifying equivalent fractions through 18 problems
Exercise 7.3 contains 12 comparison questions using various methods including cross-multiplication
Exercise 7.4 and 7.5 together comprise 35 operational questions ranging from basic to word problems
Exercise 7.6 includes 10 questions on number line plotting and 8 on decimal conversion
The chapter concludes with a mixed-revision exercise of 20 multi-concept questions

Detailed Solutions for Like and Unlike Fractions (Exercise 7.1)

Exercise 7.1 in CBSE Class 6 Mathematics Chapter 7 Fractions begins with identifying fractions from visual representations such as shaded circles and rectangles. Questions 1-5 ask students to write fractions for shaded portions, testing their ability to count parts and wholes. Questions 6-10 introduce the distinction between like fractions (denominators are identical, such as 2/7, 3/7, 5/7) and unlike fractions (denominators differ, such as 1/2, 2/3, 3/4). The NCERT approach emphasizes that like fractions can be compared simply by looking at numerators, while unlike fractions require conversion to a common denominator. Questions 11-15 present mixed sets and ask students to group them correctly. A common error students make here is confusing the numerator and denominator roles. The solutions provided in NCERT use color-coded diagrams to reinforce the concept that the denominator tells us into how many equal parts the whole is divided, while the numerator tells how many of those parts we are considering.

Mastering Equivalent Fractions (Exercise 7.2) in Class 6 Mathematics Chapter 7

Equivalent fractions represent the same value despite having different numerators and denominators. Exercise 7.2 dedicates 18 questions to this foundational concept. The NCERT method teaches two approaches: multiplication (multiply both numerator and denominator by the same non-zero number) and division (divide both by their common factor). Questions 1-6 ask students to find three equivalent fractions for given fractions like 2/3 (answers: 4/6, 6/9, 8/12). Questions 7-12 reverse the process: given one fraction in a pair, find the missing numerator or denominator to make them equivalent (e.g., 3/5 =?/20, answer: 12). Questions 13-15 use visual fraction strips to verify equivalence. The critical insight NCERT emphasizes is that equivalent fractions occupy the same position on a number line. Questions 16-18 are application problems where students must recognize equivalent fractions in real contexts (like 1/2 of a cake being the same as 3/6 of the cake). Students using CBSETUTOR.ai can upload photos of these fraction strips and receive instant verification whether their shading correctly demonstrates equivalence, making practice much more efficient than traditional methods.

To find equivalent fractions, multiply or divide numerator AND denominator by the same number
3/4 = 6/8 = 9/12 = 12/16 (multiply by 2, 3, 4 respectively)
Simplest form is found by dividing by the HCF of numerator and denominator
12/18 simplified: HCF(12,18) = 6, so 12÷6 / 18÷6 = 2/3
Visual verification: if two fractions are equivalent, their shaded areas match when wholes are equal

Comparing and Ordering Fractions: Exercise 7.3 Solutions for CBSE Class 6 Mathematics

CBSE Class 6 Mathematics Chapter 7 Fractions teaches three methods for comparing fractions in Exercise 7.3. Method 1: If fractions are like fractions, compare numerators directly (5/8 > 3/8). Method 2: If fractions are unlike, convert them to like fractions using LCM of denominators. For example, to compare 2/3 and 3/4, LCM(3,4) = 12, so convert to 8/12 and 9/12; thus 3/4 > 2/3. Method 3: Cross-multiplication for quick comparison of two fractions (multiply numerator of first by denominator of second, and vice versa). Questions 1-4 use Method 1, questions 5-9 require Method 2, and questions 10-12 mix both methods. NCERT specifically warns against the common student error of comparing numerators when denominators differ (wrongly concluding 2/3 < 3/5 by comparing 2 and 3). The chapter emphasizes that a larger denominator means smaller pieces, so 1/8 < 1/5 even though 8 > 5. The solutions include number line diagrams showing relative positions, reinforcing visual understanding alongside algorithmic skill.

Addition and Subtraction of Fractions: Exercise 7.4 Step-by-Step Solutions

Exercise 7.4 in CBSE Class 6 Mathematics Chapter 7 Fractions covers addition and subtraction in three progressive difficulty levels. Questions 1-8 deal with like fractions: simply add or subtract numerators and keep the denominator same (3/7 + 2/7 = 5/7). Questions 9-16 introduce unlike fractions requiring LCM conversion first. For instance, 1/2 + 1/3 requires finding LCM(2,3) = 6, converting to 3/6 + 2/6 = 5/6. Questions 17-22 mix proper and improper fractions, requiring students to convert improper results to mixed numbers (7/4 = 1¾). The final set (questions 23-28) are word problems: 'Rajesh ate 2/5 of a pizza and Priya ate 1/3. What fraction did they eat together?' The NCERT solution methodology always shows: (1) identify if fractions are like or unlike, (2) if unlike, find LCM and convert, (3) perform operation on numerators, (4) simplify the result to lowest terms, (5) convert to mixed number if needed. This five-step protocol, consistently applied across all 28 questions, builds systematic problem-solving habits that serve students well in CBSE examinations where marks are awarded for method even if the final answer contains a calculation error.

Addition of like fractions: a/c + b/c = (a+b)/c, then simplify
Addition of unlike fractions: find LCM of denominators, convert both, then add numerators
Subtraction follows identical rules: ensure common denominator first
Always express final answer in simplest form by dividing by HCF
Mixed numbers should be converted to improper fractions before operations, then converted back
Word problems require identifying what fraction represents which quantity before setting up the operation

Multiplication and Division of Fractions: Exercise 7.5 Complete Solutions

Exercise 7.5 extends operations in CBSE Class 6 Mathematics Chapter 7 Fractions to multiplication and division. Multiplication is more straightforward than addition: multiply numerators together and denominators together, then simplify (2/3 × 3/4 = 6/12 = 1/2). Questions 1-7 practice this direct method. Questions 8-12 involve whole numbers, which NCERT teaches to express as fractions with denominator 1 (5 × 2/7 = 5/1 × 2/7 = 10/7). Division uses the reciprocal method: to divide by a fraction, multiply by its reciprocal (2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9). Questions 13-19 drill this technique. Questions 20-24 combine multiple operations requiring BODMAS order. The NCERT solutions emphasize cross-cancellation before multiplying to keep numbers manageable: in 4/9 × 3/8, cancel the 4 and 8 (both divisible by 4), and cancel 3 and 9 (both divisible by 3) to get 1/6 directly without computing 12/72. Word problems in questions 25-28 involve real scenarios like recipe scaling (if one recipe needs 3/4 cup flour, how much for 2½ recipes?).

Representing Fractions on Number Line: Exercise 7.6 Visual Solutions

Exercise 7.6 in Class 6 Mathematics Chapter 7 teaches students to plot fractions on a number line, a skill that builds spatial understanding of fraction magnitude. The NCERT method divides the segment between two consecutive whole numbers into equal parts based on the denominator. To plot 3/5, divide the segment from 0 to 1 into 5 equal parts and mark the third division. Questions 1-5 ask students to plot given fractions. Questions 6-10 reverse the task: identify fractions marked on given number lines. This requires students to count divisions and identify the denominator, then count positions from zero to find the numerator. Questions asking students to plot 7/4 introduce improper fractions: 7/4 = 1¾, so plot between 1 and 2, specifically at the third quarter mark past 1. The visual nature of this exercise makes it particularly suitable for digital practice where students can manipulate interactive number lines. CBSETUTOR.ai's visual feedback helps students who struggle with equal spacing, a common source of errors when drawing by hand.

Number line for fraction a/b: divide unit segment into b equal parts, mark a-th part
For improper fraction like 7/3: 7/3 = 2⅓, plot one-third past the 2 mark
Equivalent fractions occupy the exact same point (1/2, 2/4, 3/6 all at same position)
Fractions between 0 and 1 are called proper fractions; beyond 1 are improper
Comparing fractions becomes visual: the fraction farther right is larger

Converting Fractions to Decimals: Bridging Concepts in CBSE Class 6 Mathematics

The final section of CBSE Class 6 Mathematics Chapter 7 Fractions introduces decimal representation, connecting to Chapter 8 (Decimals). NCERT teaches decimal conversion through division: to convert 3/4 to decimal, divide 3 by 4 to get 0.75. When the denominator is 10, 100, or 1000, conversion is direct: 7/10 = 0.7, 23/100 = 0.23. For other denominators, students perform long division. Questions 1-6 focus on fractions with denominators 10, 100, 1000. Questions 7-12 require long division for denominators like 2, 4, 5, 8 (which can be converted to equivalent fractions with denominator powers of 10). For example, 3/5 = 6/10 = 0.6. Questions 13-15 introduce fractions that yield recurring decimals (1/3 = 0.333...), though CBSE Class 6 only requires students to write up to two decimal places. The reverse process (decimal to fraction) is also covered: 0.75 = 75/100 = 3/4 after simplification. This bidirectional understanding prepares students for percentage calculations where they routinely convert between fractions, decimals, and percentages.

Common Errors and How to Avoid Them in Class 6 Mathematics Chapter 7

Through years of CBSE examination analysis, specific error patterns emerge repeatedly in CBSE Class 6 Mathematics Chapter 7 Fractions. Error 1: Adding/subtracting unlike fractions without finding common denominator (incorrectly calculating 1/2 + 1/3 = 2/5 by adding numerators and denominators separately). The NCERT solution always shows the LCM step explicitly. Error 2: Forgetting to simplify final answers, losing 1 mark per question in CBSE marking schemes that specifically instruct 'express in simplest form'. Error 3: Confusing multiplication and division rules, especially forgetting to invert the divisor (calculating 2/3 ÷ 3/4 as 2/3 × 3/4 instead of 2/3 × 4/3). Error 4: Comparing fractions by numerators alone when denominators differ. Error 5: Incorrect cancellation in multiplication (canceling numerator with numerator instead of numerator with denominator). Error 6: Misplacing fractions on number lines by not dividing segments equally. The solutions in this guide highlight these errors with margin notes explaining the correct approach. Regular practice with immediate feedback — the kind provided by CBSETUTOR.ai's AI tutor, which catches these specific errors in uploaded work — reduces error rates significantly.

Always check: are fractions like or unlike before adding/subtracting?
Simplification is not optional; it carries marks in CBSE assessments
Remember: division means multiply by reciprocal (flip and multiply)
Cross-cancellation saves time but cancel numerator with denominator, never both numerators
In word problems, identify what the whole is before calculating fractions
Number line divisions must be equal; use ruler or count carefully

Marking Scheme and Weightage for CBSE Class 6 Mathematics Chapter 7 Fractions

In the CBSE Class 6 Mathematics assessment structure for 2024-25, fractions typically account for 12-15% of the total marks across periodic tests and the annual examination. Internal assessments (40 marks total) usually include 6-8 marks from CBSE Class 6 Mathematics Chapter 7 Fractions, distributed as: 2 marks for basic operations (like fraction addition), 2 marks for comparison or equivalent fraction questions, 2 marks for word problems, and 2 marks for integrated questions combining fractions with other concepts. The annual examination (80 marks) dedicates approximately 10-12 marks to fractions, including 2-mark questions on operations, 3-mark questions on multi-step problems, and typically one 5-mark word problem involving multiple fraction operations. CBSE marking schemes award partial credit: in a 3-mark question, correct method with calculation error typically receives 2 marks. Showing work is essential; jumping directly to answers without showing LCM calculation or conversion steps results in zero marks even if the final answer is correct. Questions specifically ask 'Show your work' or 'Explain your reasoning', aligning with CBSE's competency-based assessment that values understanding over rote calculation.

NCERT Back Exercise Questions: Mixed Revision and Challenge Problems

The final exercise in CBSE Class 6 Mathematics Chapter 7 Fractions is a mixed-revision set that CBSE examiners frequently source questions from. This exercise contains 20 questions combining all topics: equivalent fractions, comparison, all four operations, number line, and decimal conversion. Questions 1-5 are concept identification (true/false and fill-in-the-blank testing definitions). Questions 6-10 require choosing appropriate methods (when to use LCM vs cross-multiplication for comparison). Questions 11-15 are multi-step computation: solve (2/3 + 3/4) × 1/2 ÷ 5/6, requiring correct order of operations. Questions 16-18 are application problems: 'A water tank is 3/5 full. After using 1/4 of the water, what fraction remains?' These require students to understand that 1/4 of 3/5 means 1/4 × 3/5, not 1/4. Questions 19-20 are extension challenges involving three or four fractions with mixed operations. NCERT recommends this exercise for comprehensive preparation before assessments. Students should attempt it under timed conditions (45 minutes) to simulate examination pressure.

Connecting CBSE Class 6 Mathematics Chapter 7 to Higher Classes and Real Applications

Mastery of CBSE Class 6 Mathematics Chapter 7 Fractions is not merely about passing Class 6 assessments; it forms the bedrock for numerous concepts in Classes 7-12. In Class 7, fractions directly extend to rational numbers (Chapter 1) and ratio-proportion (Chapter 8). In Class 8, operations on rational numbers (Chapter 1) and direct-inverse variation (Chapter 13) are impossible without fluent fraction manipulation. By Class 9, algebraic fractions in polynomials (Chapter 2) and trigonometric ratios (Chapter 8) require the same operational skills. In Class 10, probability is expressed in fractions, and similar triangles use fraction relationships. Beyond school, fractions appear in cooking (recipe scaling), construction (measurements), finance (interest calculations expressed as fractions), medicine (dosage calculations), and data analysis (proportions). NCERT intentionally uses real-world contexts in word problems to make these connections explicit. Students who view fractions merely as abstract school exercises struggle with application; those who understand fractions as a way to represent parts-of-wholes develop stronger mathematical reasoning. Parents can reinforce this by pointing out fractions in daily life: a pizza cut into 8 slices, measuring 3/4 cup of rice, or understanding that 30 minutes is 1/2 hour.

Class 7 Rational Numbers chapter is essentially fractions extended to include negative fractions
Class 8 Comparing Quantities uses fractions to express ratios, percentages, and profit-loss
Class 9 Probability chapter expresses all probabilities as fractions between 0 and 1
Class 10 Similar Triangles chapter uses fraction relationships in corresponding sides
Real-world: recipe halving/doubling, splitting bills, understanding sale discounts (1/4 off = 25% off)
Engineering and sciences use fractional coefficients extensively in formulas and equations

Practice Strategy and Preparation Timeline for Class 6 Mathematics Chapter 7

Effective preparation for CBSE Class 6 Mathematics Chapter 7 Fractions requires a structured three-week approach that NCERT pedagogy experts recommend. Week 1: Conceptual foundation (days 1-7) — Study sections 7.1-7.3, solve all examples in the textbook before attempting exercises, ensure 100% accuracy in like/unlike identification, equivalent fraction generation, and comparison. Week 2: Operations mastery (days 8-14) — Focus on exercises 7.4 and 7.5, starting with 10 questions daily and gradually increasing to 20. Maintain an error log noting which types of problems cause mistakes. Week 3: Integration and application (days 15-21) — Complete exercises 7.6 and the mixed-revision exercise, attempt word problems without referring to solutions first, practice under timed conditions. The final two days should be revision only, no new problem-solving. CBSE internal assessments typically occur 3-4 weeks after chapter completion in class, so starting personal practice the day the teacher begins the chapter creates a comfortable preparation buffer. Students using CBSETUTOR.ai can follow this schedule with the added advantage of instant doubt resolution and adaptive practice that automatically increases difficulty as accuracy improves. The AI tutor tracks which sub-topics need more practice and adjusts the problem feed accordingly, making preparation more efficient than working through textbooks linearly.

How CBSETUTOR.ai Supports Mastery of CBSE Class 6 Mathematics Chapter 7 Fractions

CBSETUTOR.ai provides an AI-powered tutor that has ingested every page of the NCERT Class 6 Mathematics textbook, including every worked example and exercise solution for Chapter 7 Fractions. When a student gets stuck on question 15 of Exercise 7.4, they can photograph their work and upload it. The AI analyzes where the error occurred — perhaps they found the LCM correctly but made a conversion mistake — and provides a targeted hint without revealing the full answer, maintaining the learning process. Unlike static solutions that simply show correct answers, the AI tutor explains why a student's approach went wrong and suggests a corrective step. For visual learners struggling with number line problems in Exercise 7.6, the AI generates interactive number lines where students can drag fraction markers to correct positions and receive instant feedback. For students who need additional practice beyond NCERT exercises, the platform generates unlimited similar problems calibrated to CBSE difficulty levels. Parents appreciate the ₹999/month flat pricing that covers all subjects for Classes 6-12 (not just Mathematics), making it economical for families with multiple children. The 3-day free trial requires no credit card, allowing parents to verify their child is actually engaging with the platform before committing financially. During the trial, students typically complete 15-20 problems across different chapters, giving a realistic sense of the tutoring effectiveness.

Frequently asked questions

Why does my child keep making errors when adding unlike fractions in CBSE Class 6 Mathematics Chapter 7 Fractions?+

The most common error is adding numerators and denominators directly without finding a common denominator first (computing 1/2 + 1/3 incorrectly as 2/5). Students need to internalize that unlike fractions require LCM conversion before any addition or subtraction. Practice with visual fraction bars helps make this concrete before moving to abstract calculation.

How many marks does CBSE Class 6 Mathematics Chapter 7 Fractions typically carry in the annual examination?+

Chapter 7 accounts for approximately 10-12 marks out of 80 in the CBSE Class 6 annual Mathematics examination, distributed across 2-mark, 3-mark, and one 5-mark question. Internal assessments allocate another 6-8 marks to this chapter, making total weightage around 18-20 marks across the year.

Are the methods taught in NCERT Class 6 Mathematics Chapter 7 Fractions the only acceptable methods in CBSE exams?+

CBSE marking schemes accept any mathematically valid method, but NCERT methods are specifically designed for Class 6 cognitive level and are what teachers expect. Using alternative methods (like decimal conversion for all comparisons) can work but may be more time-consuming and prone to errors at this level.

Should my child memorize all fraction-decimal conversions for common fractions like 1/2, 1/4, 3/4?+

Yes, memorizing about 15-20 common fraction-decimal pairs (halves, quarters, fifths, eighths, tenths) significantly speeds up problem-solving and reduces calculation errors. NCERT includes these repeatedly across exercises to encourage automatic recall. Flashcard practice over 2-3 weeks embeds these permanently.

My child understands the concepts but makes calculation errors in CBSE Class 6 Mathematics Chapter 7 Fractions. How can we fix this?+

Calculation errors often stem from weak multiplication tables or rushing through simplification. Ensure fluent recall of tables up to 20. Teach the habit of estimating before calculating (2/3 + 1/4 should be close to 1, so an answer of 11/12 is reasonable; an answer of 5/7 indicates an error). Require showing all work including intermediate steps, which makes errors visible for correction.

How is CBSE Class 6 Mathematics Chapter 7 Fractions different from what was taught in Class 5?+

Class 5 introduced basic fractions, simple equivalent fractions, and addition/subtraction of like fractions only. Class 6 extends to unlike fractions, all four operations including division, systematic comparison methods, number line visualization, and decimal conversion. The cognitive demand increases significantly, requiring more abstract thinking beyond visual models.

What is the best sequence to practice exercises in Class 6 Mathematics Chapter 7 for maximum retention?+

Follow the NCERT sequence: 7.1 (like/unlike), 7.2 (equivalent), 7.3 (comparison), 7.4 (add/subtract), 7.5 (multiply/divide), 7.6 (number line and decimals), then mixed revision. Each builds on the previous. Attempting 7.4 before mastering 7.2 leads to errors because addition of unlike fractions requires generating equivalent fractions.

Can my child use a calculator for CBSE Class 6 Mathematics Chapter 7 Fractions homework and tests?+

CBSE strictly prohibits calculators in Class 6 Mathematics assessments. Homework should also be done without calculators to build computational fluency. However, using calculators to verify answers after solving by hand is acceptable and helps students catch their own errors, building self-correction habits.

How do I know if my child has truly understood CBSE Class 6 Mathematics Chapter 7 Fractions or just memorized solutions?+

Test understanding by asking your child to explain their method verbally or apply concepts to new contexts. For example, ask why 3/8 cannot be simplified further, or how they would divide a 5-meter rope into pieces of 3/4 meter (testing whether they recognize this as division, not subtraction). True understanding enables explanation and flexible application.

What prerequisite knowledge from earlier classes does CBSE Class 6 Mathematics Chapter 7 Fractions assume?+

The chapter assumes students can fluently find LCM and HCF (Class 5), perform long division with remainders (Class 4-5), understand place value in decimals (Class 5), and recall multiplication tables up to 12 (Class 3-4). Gaps in these prerequisites cause struggles; addressing them first is essential before tackling Class 6 fractions.

Will concepts from CBSE Class 6 Mathematics Chapter 7 Fractions appear in competitive exams like NTSE or Math Olympiads?+

Absolutely. Fraction problems in NTSE and Olympiads at Class 6 level test deep conceptual understanding through multi-step problems and creative applications. Mastery of NCERT Class 6 Chapter 7 provides the foundation, but competition problems require thinking beyond textbook patterns, applying fraction concepts in geometry, number theory, and logic puzzles.

How much practice is sufficient for a typical student to master CBSE Class 6 Mathematics Chapter 7 Fractions?+

NCERT exercises contain approximately 120 questions total across all sections of Chapter 7. A typical student should solve all NCERT questions plus an additional 50-70 problems from reference books or platforms like CBSETUTOR.ai over 3-4 weeks. Mastery is reached when the student maintains 90%+ accuracy on mixed problems under timed conditions (2 minutes per 2-mark question).

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