Class 7 Maths · Chapter 8
Short answer: Class 7 Maths Ganita Prakash Chapter 8 "Working with Fractions" mein fractions ke saare operations — addition, subtraction, multiplication, division — ko conceptually aur procedurally cover kiya gaya hai, saath hi mixed numbers, reciprocals aur real-life word problems bhi shaamil hain. Ye chapter fraction ki understanding ko strengthen karta hai jo aage Number Play aur Operations with Integers jaise chapters me bhi kaam aayegi.
Class 7 Maths ki NCERT Ganita Prakash kitaab ka Chapter 8, "Working with Fractions", fractions ke poore concept ko ek naye tareeke se explore karta hai — jismein sirf rules yaad karne pe focus nahi hai, balki fractions ko visually aur logically samajhne pe zor diya gaya hai. Ye chapter, jo NCERT Class 7 Maths Ganita Prakash chapter wise solutions series ka ek important part hai, addition, subtraction, multiplication aur division of fractions — sab kuch cover karta hai, chahe wo proper fractions ho, improper fractions ho, ya mixed numbers.
Iss chapter ki practical value bahut zyada hai kyunki fractions humari daily life mein har jagah dikhte hain — recipe measurements se lekar distance calculation tak. Agar aap Working with Fractions class 7 exercise solutions dhoondh rahe hain, toh yahan har exercise ka step-by-step solution CBSE marking scheme ke hisaab se diya gaya hai, taaki aapko sirf answer hi nahi balki uska logic bhi clear ho jaaye.
Is chapter ko achhe se samajhna zaroori hai kyunki fractions ka concept aage chalke Chapter 6 Number Play class 7 maths ncert solutions aur Chapter 3 Arithmetic Expressions NCERT solutions jaise topics me bhi baar-baar use hota hai. Isliye is foundation ko strong banana bahut important hai.
Chapter 8 Summary — 5 Minute Revision
Chapter 8 "Working with Fractions" fractions ke basic recap se shuru hota hai — proper, improper aur mixed fractions ka concept revise karke, chapter dheere-dheere addition aur subtraction of fractions (same aur different denominators dono ke saath) ki taraf badhta hai. Iske baad multiplication of fractions ko area model aur repeated addition dono tareeke se samjhaya gaya hai, jisse students ko visually clarity milti hai ki fraction ka fraction lena actually matlab kya hota hai.
Chapter ka sabse challenging par important part hai division of fractions, jahan "reciprocal lekar multiply karo" wale rule ko sirf ek formula ki tarah nahi, balki uske peeche ka reasoning bhi diya gaya hai — ki division ka matlab hota hai "kitni baar fit hoti hai," aur reciprocal se multiply karna is idea ko mathematically represent karta hai.
Aakhri sections mein word problems diye gaye hain jisme fractions ko real-life situations jaise cooking, distance, time aur sharing me apply karna sikhaya jata hai. Ye chapter sirf calculation skill nahi, balki fraction-based reasoning develop karta hai jo higher classes ke algebra aur ratio-proportion topics ke liye bhi zaroori hai.
In-Text Questions — Solutions
Add: 2/5 + 3/10
LCM of 5 and 10 = 10
2/5 = 4/10
4/10 + 3/10 = 7/10
Answer: 7/10
Subtract: 7/8 − 1/4
LCM of 8 and 4 = 8
1/4 = 2/8
7/8 − 2/8 = 5/8
Answer: 5/8
Multiply: 3/4 × 2/5
3/4 × 2/5 = (3 × 2)/(4 × 5) = 6/20
Simplify: 6/20 = 3/10
Answer: 3/10
Divide: 4/5 ÷ 2/3
4/5 ÷ 2/3 = 4/5 × 3/2 (reciprocal lekar multiply karo)
= 12/10 = 6/5 = 1 1/5
Answer: 1 1/5
Convert 17/5 into a mixed number.
17 ÷ 5 = 3 remainder 2
Answer: 3 2/5
Find the reciprocal of 3 2/7.
3 2/7 ko improper fraction me convert karo: (3 × 7 + 2)/7 = 23/7
Answer: reciprocal = 7/23
Exercise Questions — Solutions (Q1–Q7)
Simplify: 5/6 + 1/3 − 1/2
LCM of 6, 3, 2 = 6
5/6 + 2/6 − 3/6 = (5+2−3)/6 = 4/6 = 2/3
Answer: 2/3 (1 mark process + 1 mark answer)
A rope is 5 3/4 m long. A piece of 2 1/2 m is cut from it. Find the length of remaining rope.
5 3/4 = 23/4, 2 1/2 = 5/2
LCM of 4 and 2 = 4 → 5/2 = 10/4
23/4 − 10/4 = 13/4 = 3 1/4 m
Answer: 3 1/4 m remaining (marking: conversion 1, subtraction 1, final answer 1)
Simplify: 2 1/3 × 1 2/5
2 1/3 = 7/3, 1 2/5 = 7/5
7/3 × 7/5 = 49/15 = 3 4/15
Answer: 3 4/15
Divide: 3 1/2 ÷ 1 3/4
3 1/2 = 7/2, 1 3/4 = 7/4
7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = 2
Answer: 2
A recipe needs 2/3 cup sugar for 1 batch. How much sugar is needed for 3 1/2 batches?
3 1/2 = 7/2 batches
2/3 × 7/2 = 14/6 = 7/3 = 2 1/3 cups
Answer: 2 1/3 cups sugar (setup 1, calculation 1, answer 1)
Which is greater: 5/6 or 7/9? Show working.
LCM of 6 and 9 = 18
5/6 = 15/18, 7/9 = 14/18
15/18 > 14/18, so 5/6 > 7/9
Answer: 5/6 is greater
Simplify: (1/2 + 1/3) ÷ (1/4 − 1/6)
1/2 + 1/3 = 3/6 + 2/6 = 5/6
1/4 − 1/6 = 3/12 − 2/12 = 1/12
5/6 ÷ 1/12 = 5/6 × 12/1 = 60/6 = 10
Answer: 10
Important Equations — Ek Nazar Me
| Operation | Rule |
|---|---|
| Same denominator addition/subtraction | a/c ± b/c = (a ± b)/c |
| Different denominator addition/subtraction | LCM nikaalo, fractions ko equivalent banao, phir add/subtract karo |
| Multiplication of fractions | a/b × c/d = (a × c)/(b × d) |
| Division of fractions | a/b ÷ c/d = a/b × d/c |
| Mixed to improper fraction | a b/c = (a × c + b)/c |
| Reciprocal | reciprocal of a/b = b/a (a ≠ 0) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Denominator add karna: students galti se 2/3 + 1/4 ko 3/7 likh dete hain — pehle LCM nikaalna zaroori hai.
- Mixed number ko improper fraction me convert kiye bina hi multiply/divide karne ki koshish karna, jisse galat answer aata hai.
- Division mein reciprocal lena bhool jaana — a/b ÷ c/d ko seedha a/b × c/d likh dena, jo galat hai.
- Final answer ko simplest form me na likhna — jaise 6/20 ko 3/10 na banana, jo marking scheme me marks katwa sakta hai.
- Word problems mein units ka dhyan na rakhna — cups, meters, ya kilogram jaisi units final answer ke saath likhna bhool jaana.
- Subtraction ke time signs ki galti karna, especially jab mixed numbers involved hon aur borrowing (regrouping) ki zaroorat pade.
Board-Style Important Questions
- Fraction addition/subtraction with unlike denominators — school-level unit tests aur term exams me commonly poocha jaata hai.
- Word problems based on recipes, distance, ya sharing quantities using fractions — application-based questions ke roop me.
- Multiplication aur division of mixed numbers ka combined problem, jahan pehle conversion phir operation karna hota hai.
- Simplification of fractional expressions with multiple operations (BODMAS ke saath fractions) — thoda tricky maana jaata hai.
- Comparing two or more fractions aur unhe ascending/descending order me arrange karna.
Aksar Poochhe Jaane Wale Sawaal
Class 7 Maths Ganita Prakash Chapter 8 'Working with Fractions' mein kya-kya topics cover hote hain?
Is chapter mein fractions ke basics ka recap, addition-subtraction of like aur unlike fractions, multiplication aur division of fractions, mixed numbers ka conversion, reciprocal ka concept, aur real-life word problems cover kiye gaye hain.
Fractions ko divide karte waqt reciprocal kyun liya jaata hai?
Division ka matlab hota hai ki ek quantity dusri quantity mein kitni baar fit hoti hai. Fraction ko divide karne ke liye us fraction ka reciprocal lekar multiply karna mathematically iss idea ko represent karta hai, isliye a/b ÷ c/d = a/b × d/c hota hai.
Mixed number ko improper fraction mein kaise convert karte hain?
Mixed number a b/c ko improper fraction mein convert karne ke liye formula use hota hai: (a × c + b)/c. Jaise 3 2/5 = (3×5+2)/5 = 17/5.
Kya Working with Fractions chapter board exam ke liye important hai?
Haan, fractions ka concept sirf iss chapter tak simit nahi hai — ye aage Number Play, Arithmetic Expressions aur higher classes ke algebra topics mein bhi use hota hai, isliye iski strong understanding zaroori hai.
Fraction word problems solve karne ka best approach kya hai?
Sabse pehle problem ko carefully padho aur identify karo ki addition, subtraction, multiplication ya division ki zaroorat hai. Mixed numbers ko improper fractions mein convert karo, phir operation perform karo, aur answer ko simplest form mein likho with correct units.
Is chapter ke exercises solve karne ke liye kaunsi common mistakes se bachna chahiye?
Denominators ko directly add karne se bacho, mixed numbers ko convert kiye bina operation na karo, division mein reciprocal lena mat bhoolo, aur final answer ko hamesha simplest form mein likho.
Class 7 Maths — Saare Chapters
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