Class 7 Maths · Chapter 10
Short answer: Chapter 10 'Operations with Integers' Class 7 Ganita Prakash mein integers (positive, negative, zero) ke saath addition, subtraction, multiplication aur division ke rules seekhte hain, number line par visualize karte hain, aur real-life applications (temperature, elevation, profit-loss) mein apply karte hain.
Class 7 Maths Ganita Prakash ke Chapter 10 Operations with Integers mein hum integers — matlab positive numbers, negative numbers aur zero — ke saath char basic operations karna seekhte hain: addition, subtraction, multiplication aur division. Ye chapter poore Class 7 number-sense ki neev hai, kyunki aage geometry, algebra jaise 'Expressions Using Letter-Numbers class 7 notes' aur 'Working with Fractions class 7 exercise solutions' mein bhi negative numbers baar-baar aayenge.
Agar aap NCERT Class 7 Maths Ganita Prakash chapter wise solutions dhoondh rahe hain, to ye page aapko step-by-step working, common mistakes, aur exam-style questions ek jagah deta hai.
Integers ka concept roz-marra ki life mein bahut jagah use hota hai — jaise temperature below zero, sea level se elevation, bank account mein profit ya loss, aur lift mein basement floor numbers negative dikhaye jaate hain. Isi wajah se ye chapter sirf exam ke liye nahi, real-world problem-solving ke liye bhi zaroori hai.
Chapter 10 Summary — 5 Minute Revision
Operations with Integers chapter integers ke number line representation se shuru hokar addition-subtraction ke rules, phir multiplication-division ke sign rules tak cover karta hai. Isme number line par jumps, additive inverse, aur BODMAS jaisi properties bhi aati hain jo mixed operations solve karne mein kaam aati hain.
Jo students 'Number Play class 7 maths ncert solutions' ya 'A Peek Beyond the Point class 7 solutions' jaise dusre chapters padh rahe hain unke liye ye integers wala foundation bahut important hai, kyunki decimal aur fraction operations mein bhi negative sign handling same logic follow karti hai.
Chapter ke through students seekhte hain ki same sign integers ko add karne par sign same rehta hai magnitude add hoti hai, jabki different sign integers ko add karne par bada number ka sign lekar difference nikala jaata hai. Multiplication-division mein: same sign = positive result, different sign = negative result — ye do rules poore chapter ki backbone hain.
In-Text Questions — Solutions
Number line par -5 se shuru karke 8 steps right chalne par kaun sa number aayega?
-5 + 8 = 3
Left se right jump positive addition dikhata hai. -5 par khade hokar 8 right steps lene se hum 3 par pahunchte hain.
(-7) + (-4) ka value nikaliye.
(-7) + (-4) = -(7 + 4) = -11
Dono integers same sign (negative) ke hain, isliye magnitudes add karke same negative sign lagate hain.
(-15) ÷ 3 ka answer kya hoga?
(-15) ÷ 3 = -5
Different sign division mein result hamesha negative hota hai.
6 × (-9) ka value batayein.
6 × (-9) = -54
Positive × negative = negative, magnitudes multiply hoti hain.
Exercise Questions — Solutions (Q1–Q6)
Simplify: (-25) + 18 + (-7) – (-10)
(-25) + 18 + (-7) - (-10)
= -25 + 18 - 7 + 10
Positive terms add karein: 18 + 10 = 28
Negative terms add karein: -25 - 7 = -32
= 28 + (-32) = -4
Answer: -4
Ek submarine samundra tal se 350 m neeche hai. Woh 120 m upar aati hai, phir 80 m aur neeche jaati hai. Uski final position kya hai (sea level ke reference mein)?
Sea level = 0, neeche jaana = negative
Starting position = -350 m
120 m upar = -350 + 120 = -230 m
80 m neeche = -230 + (-80) = -310 m
Answer: Submarine sea level se 310 m neeche hai.
Evaluate: (-8) × (-6) ÷ (-4)
BODMAS ke hisaab se left se right multiplication-division karein.
(-8) × (-6) = 48
48 ÷ (-4) = -12
Answer: -12
Ek company ko January mein ₹25,000 ka loss aur February mein ₹18,000 ka profit hua. Overall kya sthiti hai?
Loss ko negative aur profit ko positive maante hain.
Overall = (-25000) + 18000 = -7000
Answer: Company ko overall ₹7,000 ka loss hua.
Additive inverse of -34 kya hai, aur verify karein ki inka sum zero hota hai.
Additive inverse of -34 = 34
Verification: (-34) + 34 = 0
Answer: 34
Simplify using distributive property: (-12) × (25 + 5)
(-12) × (25 + 5) = (-12 × 25) + (-12 × 5)
= -300 + (-60) = -360
Cross-check: (-12) × 30 = -360 ✓
Answer: -360
Important Equations — Ek Nazar Me
| Rule | Statement | Example |
|---|---|---|
| Same-sign addition | Magnitudes add karo, same sign rakho | (-3) + (-5) = -8 |
| Different-sign addition | Bade magnitude ka sign lo, difference nikaalo | (-9) + 4 = -5 |
| Subtraction rule | a - b = a + (additive inverse of b) | 7 - (-3) = 7 + 3 = 10 |
| Same-sign multiplication/division | Result positive hota hai | (-6) × (-4) = 24 |
| Different-sign multiplication/division | Result negative hota hai | 8 × (-2) = -16 |
| Additive inverse | a + (-a) = 0 | 15 + (-15) = 0 |
| Order of operations | BODMAS follow karo mixed expressions mein | (-2) + 3 × (-4) = -2 + (-12) = -14 |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Subtraction ko simple minus samajh kar sign flip karna bhool jaate hain — yaad rakhein a - (-b) = a + b, additive inverse use karna zaroori hai.
- Do negative numbers ko multiply/divide karte waqt result ko negative likh dena — asal mein same sign ka result hamesha positive hota hai.
- Number line par jump ki direction galat lena — negative number add karne par hamesha LEFT move karte hain, right nahi.
- Mixed operations mein BODMAS follow na karna — multiplication/division ko addition/subtraction se pehle solve karna zaroori hai.
- Word problems mein 'below', 'loss', 'depth' jaise words ko negative sign se represent karna bhool jaana — isse poora answer ulta ho jaata hai.
- Zero ko positive ya negative maan lena — zero na positive hai na negative, ye ek neutral integer hai jo kisi bhi number se add karne par usi number ko wapas deta hai.
Board-Style Important Questions
- Number line ka use karke integers ki addition/subtraction visualize karna aur explain karna
- Real-life context (temperature, elevation, profit-loss) ko integer expression mein convert karke solve karna
- Multi-step mixed operation expressions (BODMAS ke saath integers) ko simplify karna
- Additive inverse aur uski property (a + (-a) = 0) verify karna
- Distributive property ka use karke integer multiplication simplify karna
- Word problem mein sahi sign (positive/negative) identify karke final answer nikalna
Aksar Poochhe Jaane Wale Sawaal
Class 7 Ganita Prakash Chapter 10 Operations with Integers mein kya seekhte hain?
Is chapter mein integers (positive, negative, zero) ke saath addition, subtraction, multiplication aur division ke rules, number line representation, additive inverse, aur real-life applications seekhte hain.
Integers ki addition aur subtraction ke basic rules kya hain?
Same sign integers add karne par magnitudes add hoti hain aur sign same rehta hai. Different sign integers add karne par bade magnitude ka sign lekar difference nikalte hain. Subtraction ke liye additive inverse add karte hain.
Do negative integers ko multiply karne par result positive kyun hota hai?
Ye ek established mathematical rule hai: same sign (dono positive ya dono negative) numbers ka product hamesha positive hota hai, jabki different sign numbers ka product negative hota hai.
Additive inverse kya hota hai?
Kisi bhi integer 'a' ka additive inverse '-a' hota hai, aur dono ko add karne par result hamesha zero aata hai, jaise 12 + (-12) = 0.
Integers ke mixed operations solve karte waqt kaunsa order follow karna chahiye?
BODMAS/PEMDAS rule follow karte hain — pehle brackets, phir multiplication/division (left se right), fir addition/subtraction (left se right).
Operations with Integers chapter real life mein kaise use hota hai?
Temperature below zero measure karne, sea level se elevation ya depth batane, bank account mein profit-loss track karne, aur lift mein basement floors dikhane jaise practical situations mein integers ka use hota hai.
Class 7 Maths — Saare Chapters
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