Class 8 Maths Rational Numbers NCERT Solutions

Rational Numbers Ka Parichay

Rational numbers—yaani wo numbers jo p/q ke roop mein likhe ja sakte hain, jahan p aur q integers hain aur q bilkul zero nahi—isee parichay ke around hi humara poora focus rahega. Is section mein hum in numbers ke basic concepts ko samjhenge, aur saath hi NCERT exercises ke solutions par bhi nazar daalenge, taaki cheezein clear ho jaayein.

Kya Padhenge Ismein

• Rational numbers ka matlab hota hai woh numbers jo do integers ke ratio ke roop mein likhe ja sakte hain. Matlab p/q format, jahan q zero nahi hota. Samajhne ke liye kuch examples le lein, jaise 1/2, 3/4, ya -5/7. Aur haan, poori integers bhi isi category mein aati hain, kyunki unhein 1 se divide karke likha ja sakta hai, jaise 5 ko 5/1. Asaan lagta hai na? Bas yahi hai — thoda sa concept pakdo, examples dekh lo, aur aage badho.
• Addition, subtraction, multiplication, division—yeh sab basic operations hain jo ismein cover honge.
• So what exactly will you find inside? Simple — the important questions from your NCERT book, all neatly solved. No fluff, no detours. Just the answers you actually need, right there.

Links for Chapter-wise Download NCERT Solution for Class 8 गणित in hindi Language

Here we have provided NCERT Solution for Class 8 गणित in hindi Language, Just select the chapters below to get solution of the same:

एक चर वाले रैखिक समीकरण

चतुर्भुजों को समझना

प्रायोगिक ज्यामिति

आंकड़ों का प्रबंधन

वर्ग और वर्गमूल

घन और घनमूल

राशियों की तुलना

बीजीय व्यंजक एवं सर्वसमिकाएँ

ठोस आकारों का चित्रण

क्षेत्रमिति

घातांक और घात

सीधा और प्रतिलोम समानुपात

गुणनखंडन

आलेखों से परिचय

संख्याओं के साथ खेलना

Rational Numbers Kya Hote Hain?

Rational numbers ko agar seedha seedha kaho toh woh numbers jo fractions ki shakal mein likhe ja sakte hain. Jaise 1/2, ya -3/4, aur haan, 5 bhi — kyunki usko 5/1 likh sakte ho. Aur yeh sirf paper par nahi rehte, number line par bhi inki jagah bilkul clear hoti hai. Real life mein toh inka chakkar har jagah hai — naap tol ho, koi cheez measure karni ho, har jagah yeh chhupe hote hain. Socho, bina fractions ke aaj ka din kaise guzarta?

Rational Numbers Ke Properties

Closure Property

Jab aap do rational numbers ko add karte hain, subtract karte hain, ya unhe aapas mein multiply karte hain—aur haan, divide bhi, lekin zero se nahi—to jo answer aata hai, wo bhi hamesha ek rational number hi hota hai. Socho, 1/2 aur 1/3 ko le lo. Unhe jod do, to 5/6 milta hai. Aur 5/6 — bilkul rational hai. Bas, yahi closure ka funda hai.

Commutative Property

Rational numbers play nice when it comes to addition and multiplication—they’re commutative. What that basically means is the order you do things in doesn’t change the result. So a + b is always the same as b + a, and a × b equals b × a, no matter which rational numbers you pick. Take 2/3 + 4/5, for instance. Flip it around to 4/5 + 2/3, and you get the exact same answer. Simple as that.

NCERT Exercise Solutions

Exercise 1.1: Basic Problems

Is exercise mein basics clear karne ka kaam hai—rational numbers ko pehchanna aur unke saath simple operations karna. Ek example lete hain: 3/4 aur -5/6 ko add karna hai. Toh pehle LCM nikalte hain — 4 aur 6 ka LCM 12 aata hai. Ab 3/4 ko hum 9/12 likh sakte hain, aur -5/6 ko -10/12. Ab bas add karo: 9/12 + (-10/12) = -1/12. Simple hai, bas LCM ka dhyan rakho.

Exercise 1.2: Advanced Applications

Yahan par kuch word problems hain jo real-life scenarios par based hain. Socho, ek field ka 3/5 hissa already cultivated hai. Ab agar hum 1/4 hissa aur cultivate kar lein, toh total kitna hissa cultivated ho jayega? Iska hal bahut simple hai—pehle dono fractions ko add karna hoga. 5 aur 4 ka LCM 20 aata hai. Toh 3/5 ko hum 12/20 mein badal dete hain, aur 1/4 ko 5/20 mein. Ab inko jod do: 12/20 + 5/20 = 17/20. Bas, itna hi!

Practice Tips for Students

Rational numbers really click when you practice them regularly—there’s no shortcut around it. Work through those NCERT exercises one step at a time, no rushing. If something feels fuzzy, go back and stare at the examples again, maybe twice. And hey, don’t be shy about asking for help, whether that’s from your teacher or digging through online resources. A little patience goes a long way here.

Common Mistakes to Avoid

Okay, here is the rewritten paragraph, keeping it conversational, varied. Perfectly on-topic for "Common Mistakes to Avoid." --- You’d be surprised how many students trip up on this one—they just forget that a denominator can never be zero. Plain and simple. It’s a hard rule, and there’s no getting around it. And then, of course, you’ve got the classic division move: you flip that fraction and multiply. Somehow it slips your mind right in the heat of the moment. Slow down — double-check. And don’t even get me started on negative signs. One little minus sign can throw your whole answer off if you’re not paying close attention. Keep your wits about you when those come into play.

Conclusion

Rational numbers—yeh chapter class 8 maths mein koi mamuli nahi hai, bilkul important hai. Aur dekho, yeh sirf is saal ke liye nahi hai; aage ki classes mein bhi tumhe iski zaroorat padegi, baar baar. Toh abhi agar concepts thode bhi dhunde hain, toh samajh lo problem baad mein pakki hai. Isliye, time laga ke practice karo, sawaalon ko jhelo. Aur haan, NCERT solutions ka sahaara lo—usse confidence aise banega jaise dum par dum lagta hai.