Arithmetic expression kya hota hai?

Sankhyaon aur operation ke chinhon se bana ganit ka vaakya, jaise 13 + 2, 20 − 4, 12 × 5 ya 18 ÷ 3. Har expression ki ek value hoti hai, wo sankhya jo use hal karne pe milti hai, aur barabar ka chinh dono ko jodta hai: 13 + 2 = 15. Alag expressions ki value ek ho sakti hai: 10 + 2, 15 − 3, 3 × 4 aur 24 ÷ 2, sab 12 hain.

Expression ko kis kram mein hal karna chahiye?

Pehle brackets ke andar ka hisaab karo. Phir har ghatav ko inverse jodne ki tarah likhkar expression ko terms mein todo, yaani + se jude hisson mein. Har term ki value nikaalo, jisme × aur ÷ ho sakte hain, aur terms jodo. 5 × (3 + 2) + 7 × 8 + 3 ke liye ye 25 + 56 + 3 = 84 deta hai.

Do expressions ki tulna bina hal kiye kaise karein?

Dekho ki unke hisse kaise alag hain. 1023 + 125 aur 1022 + 128 mein pehla 1 upar se shuru hota hai par 3 kam jodta hai, isliye 2 chhota hai. 113 − 25 aur 112 − 24 mein pehla 1 upar se shuru hota hai aur 1 zyaada ghataata bhi hai, isliye dono barabar hain. Marbles milne ya khone ki kalpana se madad milti hai.

Expressions ki value kaise nikalein?

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Expressions aur unki value

13 + 2, 20 − 4, 12 × 5 aur 18 ÷ 3 jaise vaakya arithmetic expressions hain. Har ek ki ek value hoti hai, wo sankhya jo hal karne pe milti hai, aur dono ko barabar ke chinh se jodte hain: 13 + 2 = 15. 13 + 2 ko “13 plus 2” ya “13 aur 2 ka jod” padh sakte ho, aur 5 × 25 ko “5 guna 25” ya “5 aur 25 ka guna-phal”.

Alag expressions ki value ek ho sakti hai. Koi pasandeeda sankhya lo, jaise 24, aur use kai tarah likho: 12 + 12, 30 − 6, 4 × 6, 48 ÷ 2. Asli sthitiyon waale expressions bhi utne hi kaam ke hain: Mallika ka school ka lunch roz ₹25 ka hai, to Monday se Friday tak ka kharch 5 × 25 rupaye hai.

Bina hisaab ke tulna

Sankhyaon ki tarah expressions ki tulna bhi =, < aur > se unki value ke hisaab se hoti hai: 10 + 2 > 7 + 1, kyunki 12, 8 se zyaada hai. Par aksar dono value nikaalne se jaldi ka raasta hota hai.

1023 + 125 aur 1022 + 128 mein kaunsa bada hai? Socho, Raja ke paas 1023 marbles hain aur use 125 aur milte hain, aur Joy ke paas 1022 hain aur use 128 milte hain. Raja shuruaat mein 1 aage hai, par Joy ko aaj 3 zyaada milte hain, isliye aakhir mein Joy 2 aage hai: 1023 + 125 < 1022 + 128. Ab 113 − 25 aur 112 − 24 dekho. Raja ke paas 1 marble zyaada tha, par 1 zyaada khoya bhi, isliye dono ke paas utne hi bache: 113 − 25 = 112 − 24.

Marbles ki pattiyan: Raja ke paas 1 extra aur Joy ke paas 3 extra, isliye 1023 + 125 < 1022 + 128; Raja ka extra marble phir kho jaata hai, isliye 113 − 25 = 112 − 24 — Bina hal kiye tulna

Ek expression, do matlab

Chapter ke ek English vaakya mein Shalini ek dost ke bagal mein hai aur khilaune bhi hain, par saaf nahi ki khilaune dost ke hain ya Shalini ke; ek comma ye tay karta hai. Expressions bhi aise hi uljha sakte hain. Mallesh ke paas 30 marbles the aur Arun ke paas 4-4 marbles waale 5 thaile, to Mallesh ne likha 30 + 5 × 4. Purna ko kahaani nahi pata thi aur usne pehle joda: 30 + 5 = 35, phir 35 × 4 = 140. Mallesh ne pehle guna kiya: 5 × 4 = 20, phir 30 + 20 = 50. Mallesh sahi hai, par sirf expression dekhkar ye pata nahi chalta. Ise saaf karne ke liye ganit mein do auzaar hain: brackets aur terms.

Purna ka (30 + 5) × 4 = 140 galat hai; Mallesh ka 30 + (5 × 4) = 50, 30 marbles aur 4 ke 5 thailon se mel khaata hai — 30 + 5 × 4: kaunsa tareeka sahi?

Pehle brackets

Brackets ke andar jo hai, wo sabse pehle hal hota hai, isliye 30 + (5 × 4) = 30 + 20 = 50. Paison ke sawaalon mein bhi brackets zaroori hain. Irfan ne ₹15 ke biscuit aur ₹56 ki toor dal li aur ₹100 ka note diya. Use 100 − (15 + 56) = 100 − 71 = 29 rupaye waapas milenge. Brackets ke bina 100 − 15 + 56 = 141 aata, jo diye gaye paise se bhi zyaada hai, aur iska koi matlab nahi.

Baaki terms tay karte hain

Jab brackets nahi batate ki pehle kya karna hai, tab terms batate hain. Terms expression ke wo hisse hain jo + chinh se jude hote hain; ghatav ko inverse jodne ki tarah likhte hain, to 30 − 4 ban jaata hai 30 + (−4). Guna ya bhaag ek hi term hota hai. Kisi bhi expression ko hal karne ka tareeka: brackets hal karo, har term hal karo, phir terms jodo. Jaise 5 × (3 + 2) + 7 × 8 + 3 ke terms 5 × (3 + 2), 7 × 8 aur 3 hain, jinki value 25, 56 aur 3 hai, to kul value 84 hai.

5 × (3 + 2) + 7 × 8 + 3 ke teen step: brackets se 5 × 5 + 7 × 8 + 3, terms 25, 56 aur 3, aur jod 84 — Brackets, phir terms, phir jod

Sthitiyon ke liye expressions

Chaar doston ne ₹23 waale dose khaaye aur ₹5 tip di: 4 × 23 + 5 = 92 + 5 = 97 rupaye, jiske terms 4 × 23 aur 5 hain. Ek khel mein teacher 5 bole to 33 khilaadi 5-5 ke group banaate hain: chhe group aur 3 bahar, isliye Ruby ne likha 6 × 5 + 3. Raghu ne 100 kg chaawal 2 kg ke packet mein bhara aur 4 packet pehle se the, to kul 4 + 100 ÷ 2 packet hain. Tasveeron ko bhi aise hi padhte hain: 2-2 ke paanch column aur 3 ka ek column 5 × 2 + 3 = 13 hai, par 5 + 3 ke do column 2 × (5 + 3) = 16 hain.

33 khilaadi 5 ke group mein: chhe group aur 3 bahar, 6 × 5 + 3; 4 ke group se 8 × 4 + 1 aur 7 ke group se 4 × 7 + 5 — 33 khilaadi, 5 ke group

2 hare squares ke paanch column aur 3 laal squares ka ek column 5 × 2 + 3 = 13; 5 peele aur 3 neele squares ke do column 2 × (5 + 3) = 16 — Kaunsi tasveer 5 × 2 + 3 hai?

Ye kyun zaroori hai

Jab sab ek expression ko ek hi tarah padhte hain, tabhi bill, recipe aur spreadsheet ka ek sahi jawab aata hai. Terms, jagah badalna aur brackets hatana terms aur brackets mein seekho, aur jod ka guna distributive property kya hai mein. Kitaab ke har sawaal ka jawab Chapter 2 ke NCERT solutions mein hai; poore Chapter 2 ke notes bhi dekho.