Class 8 Maths · Chapter 6
Short answer:
Distributive property: a × (b + c) = a×b + a×c aur a × (b − c) = a×b − a×c. Ye Chapter 6 "We Distribute, Yet Things Multiply" (Ganita Prakash Class 8, Part 1) ka core idea hai — expression ko todo (distribute karo), result multiplication jaisa hi milta hai. Mental maths, algebra expansion aur factorisation — teeno jagah use hota hai.
Chapter 6 "We Distribute, Yet Things Multiply" Ganita Prakash Class 8 Part 1 ka ek foundational chapter hai jo distributive property ko explore karta hai — ye idea ki multiplication ko numbers ke groups ke upar "distribute" kiya ja sakta hai bina final result badle. Title khud is paradox ko capture karta hai: hum expression ko todte (distribute karte) hain, lekin end me multiplication ka result hi milta hai. Ye chapter mental maths shortcuts, algebra ki expansion/factorisation, aur real-life quantity calculations — sabme kaam aata hai. Agle chapters jaise Algebra Play aur Fractions in Disguise me yehi property baar-baar use hoti hai, isliye is chapter ki grip mazboot honi chahiye.
Chapter 6 Summary — 5 Minute Revision
Is chapter me humne seekha ki distributive property kaise numbers ko groups me tod kar calculation aasan banati hai — chahe wo mental maths ho (47×102 jaisa fast trick), algebra ki expansion (6(x+5) = 6x+30), ya factorisation (12x+18y = 6(2x+3y)). Sign rules ka dhyan rakhna sabse zaroori hai, especially negative brackets ke saath. Ye property sirf ek formula nahi, balki poore algebra ki neev hai jo aage Algebra Play aur Fractions in Disguise jaise chapters me kaam aayegi. Ganita Prakash ke naye do-part (Part 1: chapters 1-7, Part 2: chapters 8-14) structure me ye Part 1 ka chhata chapter hai.
In-Text Questions — Solutions
Kya 5 × (6 + 4) aur (5 × 6) + (5 × 4) ka answer same hoga?
Haan, dono ka answer 50 hi aayega. 5 × (6+4) = 5 × 10 = 50, aur (5×6)+(5×4) = 30+20 = 50. Yehi distributive property ka core demonstration hai.Kya subtraction me bhi distributive property verify hoti hai — jaise 7 × (10 − 3)?
Haan. LHS: 7 × 7 = 49. RHS: 7×10 − 7×3 = 70 − 21 = 49. Dono match karte hain, isliye subtraction ke liye bhi ye property sahi hai.Agar a(b+c) = ab+ac hai, toh kya a(b+c+d) ke liye bhi same pattern chalega?
Bilkul chalega — distributive property kitne bhi terms ke sum pe apply hoti hai: a(b+c+d) = ab+ac+ad. Ye pattern har additional term ke saath extend hota rehta hai.Exercise Questions — Solutions (Q1–Q6)
Distributive property use karke solve karo: 47 × 102
47 × 102 = 47 × (100 + 2)
= 47 × 100 + 47 × 2
= 4700 + 94 = 4794
Marking scheme: split karne ka step (1 mark) + dono products (1 mark) + final answer (1 mark).
6(x + 5) ko expand karo aur x = 3 ke liye value nikaalo.
6(x + 5) = 6 × x + 6 × 5 = 6x + 30
x = 3 pe:
6(3) + 30 = 18 + 30 = 48
Verify: 6(3+5) = 6 × 8 = 48. Match ho gaya.
Factorise karo: 12x + 18y
Dono terms ka HCF nikaalo — 12 aur 18 ka HCF = 6.
12x + 18y = 6(2x + 3y)
Check: 6 × 2x = 12x, 6 × 3y = 18y ✓
Ek dukaan me pen ki price ₹8 hai. Agar Meera 3 packet leti hai jisme har packet me (5 + 2) pen hain, toh distributive property se total pens aur total cost nikaalo.
Har packet me pens = 5 + 2 = 7
3 × (5 + 2) = 3 × 5 + 3 × 2 = 15 + 6 = 21 pens
Total cost = 21 × 8 = ₹168
Ya seedha: 3 × 7 × 8 = 168, dono tareeke se same answer aata hai — yehi distributive property ka fayda hai.
Verify karo ki subtraction ke liye bhi distributive property chalti hai: 9 × (15 − 5)
LHS:
9 × (15 − 5) = 9 × 10 = 90
RHS:
9 × 15 − 9 × 5 = 135 − 45 = 90
LHS = RHS = 90, isliye a × (b − c) = a×b − a×c bhi sahi hai.
−4(x − 7) ko simplify karo aur sign ki galti se bacho.
−4(x − 7) = (−4 × x) + (−4 × −7)
= −4x + 28
Common mistake: log −4 × −7 ko −28 likh dete hain, par negative × negative = positive, isliye +28 hi sahi hai.
Important Equations — Ek Nazar Me
| Rule | Formula | Note |
|---|---|---|
| Distributive law (addition) | a × (b + c) = a×b + a×c | Chapter ka core idea |
| Distributive law (subtraction) | a × (b − c) = a×b − a×c | Negative sign ka dhyan rakho |
| Reverse (factorisation) | ab + ac = a(b + c) | Common factor nikaalna |
| Division distribution | (b + c) ÷ a = b/a + c/a | Sirf numerator me sum ho tab |
| Sign rule | (−) × (−) = (+), (−) × (+) = (−) | Negative bracket expand karte waqt |
| Mental-maths shortcut | a × (round number ± small) = fast calculation | Jaise 47 × 102 = 47×100 + 47×2 |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Negative bracket expand karte waqt sign ki galti — jaise −4(x−7) ko −4x−28 likh dena, jabki sahi answer −4x+28 hai (negative × negative = positive)
- Distributive property ko division a/(b+c) pe bhi apply kar dena, jo generally galat hai — ye sirf (b+c)/a form me sahi kaam karta hai, a/(b+c) ≠ a/b + a/c
- Factorisation karte waqt common factor poora na nikaalna — jaise 12x+18y ko 3(4x+6y) likh dena jabki HCF 6 hai aur poora factor 6(2x+3y) hona chahiye
- Mental maths shortcut me splitting ke baad ek term multiply karna bhool jana — jaise 47×102 ko 47×100 tak calculate karke 47×2 add karna bhool jana
- Expand karte waqt bracket ke andar sirf pehle term ko outer number se multiply karna aur doosre term ko as-it-is chhod dena
- Verification skip kar dena — LHS aur RHS dono nikaal ke match check na karna, jisse silly calculation errors pakde nahi jaate
Board-Style Important Questions
- Class 8 board-level assessments me distributive property ke mental-maths application wale questions poochhe jaate hain, jaise bade numbers ko round-off karke multiply karna (evidence ⬜ not found — specific exam paper/year verify nahi ho paya is session me)
- Algebraic expansion aur factorisation ke combined questions is chapter se linked hote hain — bracket expand karo phir simplify karo type problems
- Real-life word problems jisme total quantity distributive property se do tareekon se calculate karke verify karayi jaati hai
- Sign rules (negative × negative) ki understanding test karne wale short-answer questions
- Reverse process — factorisation dwara common factor nikaalne wale questions bhi practice ke liye common hain
Aksar Poochhe Jaane Wale Sawaal
Class 8 Maths chapter 'We Distribute, Yet Things Multiply' kis Ganita Prakash part me aata hai?
Ye chapter Ganita Prakash Class 8 Part 1 ka hai (chapters 1 se 7 tak Part 1 me hain, 8 se 14 Part 2 me). Naye rationalised 2026-27 syllabus me poori Class 8 Maths ab do parts me split ho gayi hai, purani single-book format ki jagah.
Distributive property ka basic formula kya hai?
Sabse basic form hai a × (b + c) = a×b + a×c, aur subtraction ke liye a × (b − c) = a×b − a×c. Chapter ka title isi idea ko pakadta hai — hum numbers ko 'distribute' karte hain, lekin result multiplication ki tarah hi behave karta hai, isliye 'Things Multiply.'
Kya distributive property sirf addition ke saath kaam karti hai?
Nahi. Ye addition aur subtraction dono ke saath kaam karti hai — a(b+c) = ab+ac aur a(b−c) = ab−ac. Division ke saath bhi ek-tarfa distributive property chalti hai jab numerator me sum ho, jaise (b+c)/a = b/a + c/a, lekin a/(b+c) generally a/b + a/c ke barabar nahi hota — ye ek common confusion hai.
Yeh chapter mental maths me kaise madad karta hai?
Jaise 47 × 102 ko seedha multiply karne ke bajaye 47 × (100+2) likh ke 4700 + 94 = 4794 turant nikal sakte ho. Isi tarah 99 × 8 ko (100−1) × 8 = 800 − 8 = 792 likh ke fast solve kar sakte ho. Distributive property speed-maths ka core trick hai.
Class 8 Maths ke naye NCERT book ka naam kya hai 2026-27 session ke liye?
Naye rationalised syllabus me Class 8 Maths ki book ka naam 'Ganita Prakash' hai, jo do parts me aati hai — Part 1 (chapters 1-7) aur Part 2 (chapters 8-14). Ye purani single-volume NCERT Mathematics book se alag structure hai.
Is chapter ko algebra ke saath kaise connect karein?
Distributive property algebra ki expansion aur factorisation dono ki neev hai. Jab tum 6(x+5) ko 6x+30 me expand karte ho ya 12x+18y ko 6(2x+3y) me factorise karte ho, dono jagah yehi property use hoti hai — isliye is chapter ko theek se samajhna aage Algebra Play chapter ke liye zaroori hai.
Class 8 Maths — Saare Chapters
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