Class 6 Maths · Chapter 7
Short answer: Class 6 Maths Ganita Prakash Chapter 7 'Fractions' me students proper, improper aur mixed fractions, equivalent fractions, simplest form, comparison aur addition-subtraction seekhte hain — poori tarah step-by-step solutions, formulas table aur common mistakes ke saath yahan diya gaya hai.
Chapter 7 poore Class 6 Maths ki number-sense building me ek bahut important step hai — yahan se students seekhte hain ki poore numbers ke alawa bhi numbers exist karte hain jo kisi whole ke 'part' ko represent karte hain. Ganita Prakash textbook (NCERT ka current rationalised syllabus, 2026-27 session) me Fractions chapter proper/improper/mixed fractions, equivalent fractions, simplest form, comparison aur addition-subtraction jaise core concepts cover karta hai. Ye chapter sirf apne aap me important nahi hai — aage chalke decimals, ratio-proportion, aur algebra jaise chapters isi foundation par khade hote hain, isliye har concept ko step-by-step samajhna zaroori hai, sirf formula rata lena kaafi nahi hoga.
Chapter 7 Summary — 5 Minute Revision
Class 6 Maths Chapter 7 'Fractions' students ko sikhata hai ki fraction kisi whole ka part represent karta hai, aur iske proper, improper, mixed types hote hain jinhe aapas me convert kiya ja sakta hai. Equivalent fractions ka concept samajhna zaroori hai kyunki isi se simplest form aur comparison dono nikalte hain — simplest form HCF se aati hai, aur different-denominator fractions ko compare/add/subtract karne ke liye pehle LCM nikaal kar unhe same denominator me convert karna padta hai. Number line par fractions ko plot karna unki relative position samajhne me madad karta hai, especially improper fractions ke case me jo 1 se aage bhi ja sakti hain. Ye saare concepts sirf is chapter tak limited nahi hain — decimals, percentages, ratio-proportion aur algebra jaise aage ke topics isi foundation par based hain, isliye practice ke through in concepts ko thoroughly clear karna zaroori hai, sirf formulas yaad karna kaafi nahi hai.In-Text Questions — Solutions
Fig 7.1 me diya gaya circle 4 equal parts me divided hai, jisme 1 part shaded hai — shaded fraction kya hai?
Total parts = 4, Shaded parts = 1.
Fraction = 1/4
Ek pizza ko 8 equal slices me kaata gaya. Agar 3 slices khaye ja chuke hain, to kitna pizza bacha hai fraction me?
Total slices = 8, Khaye gaye = 3, Bache = 8 − 3 = 5
Bacha hua pizza = 5/8
3/4 aur 6/8 equivalent fractions hain ya nahi, check karo.
Cross multiplication se check karo: 3×8 = 24, 4×6 = 24
Dono equal hain, isliye 3/4 = 6/8 (equivalent hain)
1/2 ko number line par darshane ke liye kya karna hoga?
0 aur 1 ke beech ki line ko 2 barabar hisson me baanto. Beech ka point 1/2 ko represent karega.
0 ---------•--------- 1 (beech ka point = 1/2)
Exercise Questions — Solutions (Q1–Q14)
7.1 Q1: Write the fraction representing the shaded portion — a rectangle divided into 8 equal parts with 5 parts shaded.
Total equal parts = 8, Shaded parts = 5.
Fraction = 5/8
Answer: 5/8
7.1 Q2: Colour the fractional part: (a) 1/6 of a circle divided into 6 parts (b) 6/8 of a rectangle divided into 8 parts.
(a) 1 out of 6 equal parts colour karo.
1/6
(b) 6 out of 8 equal parts colour karo.
6/8 = 3/4
7.2 Q1: Represent 5/9 on the number line.
0 aur 1 ke beech ki line ko 9 barabar bhagon me baanto. 5th point 5/9 dikhayega.
0 ----|----|----|----|--•--|----|----|----|---- 1 (5th mark = 5/9)
7.2 Q2: Represent 8/5 on the number line.
8/5 improper fraction hai, isliye 1 se aage jayega.
8/5 = 1(3/5) → 0 aur 2 ke beech, 5 equal parts me baant kar 8th mark tak jao.
7.3 Q1: Write the fractions and pair up equivalent fractions from each row: (a) 2/4 (b) 3/6 (c) 4/6 (d) 6/9.
Har fraction ko simplest form me convert karo:
2/4 = 1/2, 3/6 = 1/2, 4/6 = 2/3, 6/9 = 2/3
Equivalent pairs: (2/4, 3/6) aur (4/6, 6/9)
7.3 Q2: Replace ▢ with the correct number: 2/3 = 8/▢.
2/3 ko equivalent fraction me convert karna hai jiska numerator 8 ho.
2 × 4 = 8, isliye denominator bhi 4 se multiply hoga: 3 × 4 = 12
Answer: ▢ = 12, so 2/3 = 8/12
7.4 Q1: Find the simplest form of 36/48.
HCF of 36 and 48 nikaalo.
36 = 2×2×3×3, 48 = 2×2×2×2×3 → HCF = 12
36÷12 / 48÷12 = 3/4
Answer: 3/4
7.5 Q1: Compare 3/5 and 5/7 using cross multiplication.
Cross multiply: 3×7 = 21, 5×5 = 25
21 < 25, isliye 3/5 < 5/7
Answer: 3/5 < 5/7
7.5 Q2: Arrange in ascending order: 1/2, 1/3, 1/4, 1/6.
Same numerator hone par, jitna bada denominator utni chhoti fraction.
1/6 < 1/4 < 1/3 < 1/2
7.6 Q1: Add: 2/9 + 3/9.
Same denominator hai, sirf numerators add karo.
2/9 + 3/9 = 5/9
7.6 Q2: Add: 1/4 + 1/6.
LCM of 4 and 6 = 12.
1/4 = 3/12, 1/6 = 2/12
3/12 + 2/12 = 5/12
7.6 Q3: Subtract: 5/6 − 1/3.
LCM of 6 and 3 = 6.
1/3 = 2/6
5/6 − 2/6 = 3/6 = 1/2
7.6 Q4: Simplify: 1(2/3) + 2(1/4) (mixed fractions).
Improper fraction me convert karo: 1(2/3) = 5/3, 2(1/4) = 9/4
LCM of 3 and 4 = 12
5/3 = 20/12, 9/4 = 27/12
20/12 + 27/12 = 47/12 = 3(11/12)
7.7 Word problem: A rope is 7/8 m long. Radha cuts off 1/4 m from it. What length of rope is left?
Given: Total length = 7/8 m, cut off = 1/4 m
LCM of 8 and 4 = 8
1/4 = 2/8
Remaining = 7/8 − 2/8 = 5/8 m
Answer: 5/8 m rope bacha.
Important Equations — Ek Nazar Me
| Concept | Formula / Rule | Example |
|---|---|---|
| Fraction definition | Fraction = Numerator / Denominator (part / whole) | 3/4 — 3 parts out of 4 |
| Proper fraction | Numerator < Denominator | 2/5, 3/7 |
| Improper fraction | Numerator ≥ Denominator | 7/5, 9/4 |
| Mixed to Improper | (Whole × Denominator + Numerator) / Denominator | 2(1/3) = (2×3+1)/3 = 7/3 |
| Equivalent fractions | Numerator aur Denominator ko same number se multiply/divide karo | 2/3 = (2×2)/(3×2) = 4/6 |
| Simplest form | Numerator aur Denominator ko unke HCF se divide karo | 36/48 ÷ 12 = 3/4 |
| Comparing (same denominator) | Jiska numerator bada, woh fraction badi | 5/7 > 3/7 |
| Comparing (cross multiplication) | a/b vs c/d → a×d vs c×b compare karo | 3/5 vs 5/7 → 21 < 25 so 3/5<5/7 |
| Addition/Subtraction (same denominator) | a/c ± b/c = (a±b)/c | 3/8 + 2/8 = 5/8 |
| Addition/Subtraction (different denominator) | LCM nikaalo, fractions ko equivalent banao, phir add/subtract karo | 1/4 + 1/6 = 3/12 + 2/12 = 5/12 |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Different denominators wale fractions ko directly add/subtract kar dena bina LCM nikaale — jaise 1/2 + 1/3 ko galat tarike se 2/5 likh dena, jabki sahi answer 5/6 hai.
- Equivalent fraction banate waqt sirf numerator ya sirf denominator ko multiply karna, dono ko same number se multiply na karna.
- Simplest form nikaalte waqt HCF ki jagah kisi bhi common factor se divide kar dena aur fraction poori tarah simplify na hona (jaise 36/48 ko sirf 18/24 tak leke rukna, 3/4 tak na pahunchna).
- Mixed fraction ko improper fraction me convert karte waqt formula galat apply karna — whole number ko denominator se multiply karna bhool jaana.
- Comparing fractions me bade denominator ko badi fraction samajh lena — jabki same numerator ho to chhote denominator wali fraction badi hoti hai (jaise 1/3 > 1/5).
- Number line par improper fraction represent karte waqt sirf 0-1 ke beech dhoondhna, ye bhool jaana ki improper fraction 1 se aage bhi ja sakti hai.
Board-Style Important Questions
- School-level test me common: 'Simplify 24/36 to its lowest terms and show your working.' — HCF method se poora step dikhana zaroori hota hai marking scheme ke hisaab se.
- Frequently asked practice type: 'Arrange the following fractions in descending order: 2/3, 5/6, 1/2, 3/4' — LCM based comparison ka application.
- Word problem style (common in worksheets): 'A tank is 3/4 full. If 1/8 of the water is used, what fraction of the tank is left?' — real-life application of subtraction of fractions.
- Conceptual question often practiced: 'Represent 11/4 on the number line and convert it into a mixed fraction.' — combines number line skill with mixed fraction conversion.
- Comparison-based practice question: 'Which is greater: 5/9 or 7/12? Show by cross multiplication method.' — tests cross-multiplication comparison technique.
- Application question common in class tests: 'Ramesh reads 2/5 of a book on Monday and 1/4 on Tuesday. What fraction of the book has he read in total?' — addition of unlike fractions in word-problem form.
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths chapter 7 Fractions kis textbook me hai — Ganita Prakash ya purani Mathematics book?
Ye chapter current NCERT Class 6 Maths textbook Ganita Prakash (NEP-aligned, rationalised, 2026-27 session) ka Chapter 7 hai. Purani 14-chapter 'Mathematics' book me fractions ka number alag tha — agar aapke paas old edition hai to chapter number match nahi karega.
Fraction aur proper/improper/mixed fraction me kya farak hai?
Fraction ek whole ka part represent karta hai (a/b form me). Jab numerator < denominator ho to proper fraction (jaise 3/5). Jab numerator ≥ denominator ho to improper fraction (jaise 7/5). Improper fraction ko whole number + proper fraction me likha jaye to woh mixed fraction banti hai (jaise 1(2/5)).
Fractions ko add/subtract karne se pehle denominator same karna kyun zaroori hai?
Fraction ka matlab hai kisi whole ko kitne barabar hisson me baanta gaya. Agar denominators alag hain, matlab dono fractions alag size ke 'units' represent kar rahe hain — unko directly add nahi kar sakte. LCM nikaal kar dono ko same denominator (same unit size) me convert karna padta hai, tabhi numerators ko sahi tarike se add/subtract kiya ja sakta hai.
Simplest form (lowest terms) me fraction likhna kyun zaroori hai exams me?
CBSE marking scheme me agar answer ki simplest form nahi di jaye to kabhi kabhi step marks kat sakte hain, especially jab question explicitly 'simplest form me likho' bole. Simplest form se answer clean aur standard bhi lagta hai, aur aage ke calculations (jaise comparison ya further operations) me aasani hoti hai.
Fractions chapter Class 6 ke baad kaha kaha use hota hai — kya ye sirf ek chapter tak limited hai?
Nahi, fractions ka concept aage bahut chapters ki neev hai — decimals, percentages, ratio-proportion, algebra (jaise x/2 = 5 type equations), aur higher classes me trigonometry/probability tak fractions ka use hota rehta hai. Isliye is chapter ki understanding pakki hona zaroori hai.
Class 6 Maths ke doosre chapters jaise Prime Time ya Perimeter and Area kaise related hain Fractions se?
Directly related nahi hain but conceptually overlap hota hai — jaise Perimeter and Area chapter me kabhi kabhi fractional measurements (jaise 3(1/2) cm side) aate hain jahan fraction operations chahiye hote hain. Prime Time chapter me factors/multiples ka concept fractions ki simplest form nikaalne me (HCF use hota hai) directly kaam aata hai.
Class 6 Maths — Saare Chapters
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