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ല.സാ.ഗു. (LCM), ഉ. സാ. ഘ. (HCF)
*രണ്ടോ അതിലധികമോ സംഖ്യകളുടെ ഏറ്റവും ചെറിയ പൊതുഗുണിതമാണ് അവയുടെ ലസാഗു (ലഘുതമ സാധാരണ ഗുണിതം)
ഉദാ:
*3, 4, 5 ഇവ കൊണ്ട് നിശ്ശേഷം ഹരിക്കാവുന്ന ഏറ്റവും ചെറിയ സംഖ..................

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സംഖ്യാശ്രേണി:
*തന്നിരിക്കുന്ന സംഖ്യകൾ ഏത് ശ്രേണിയിൽ ആണ് അടുക്കിയിരിക്കുന്നതെന്ന് അവയെ സൂക്ഷ്മമായി നിരീക്ഷിക്കുന്നതിലൂടെ മനസ്സിലാക്കാവുന്നതാണ്.
ഉദാ: 1) 6, 8, 12, 7, 18, 6, __ ഈ ശ്ര..................

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സർവ്വ സമവാക്യങ്ങൾ (Identities) സൂത്രവാക്യങ്ങൾ 
1.(ab)^2  = a^2  b^2  2ab

2.(a-b)^2  = a^2b^2 - 2ab

3.(ab)^2-(a-b)^2 = 4ab

4.(ab)^2(a-b)^2 = 2 (a^2b^2)

5.a^2 - b^2 = (ab) (ab)

6.a^2  b^2 = ½[(ab)^2(a-b)^2]

7.1/a  1/b = ab/ab

8.(ab)^3 = a^3 - 3a^2b3ab^2  b^3

9.(a-b)^3 = a^3 - 3a^2b3ab^2 - b^3

10.(ab)^3(..................

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 ല . സാ.ഗു  രണ്ടോ അതിലധികമോ സംഖ്യകളുടെ ഏറ്റവും ചെറിയ പൊതു ഗുണിതമാണ് അവയുടെ ലസാഗു, (ലഘുതമ സാധാരണ ഗുണിതം) ഉ . സാ . ഘ  രണ്ടോ അതിലധികമോ സംഖ്യകളുടെ ഏറ്റവും വലിയ പൊതു ഘടകമാണ..................

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2 മുതൽ 10 വരെയുള്ള സംഖ്യയുടെ എളുപ്പരീതിയിലുള്ള  ഹരണം  ഒരു  സംഖ്യയുടെ അവസാനത്തെ രണ്ട് അക്കം 0,2,4,6,8 ഇവ വന്നാൽ ആ സംഖ്യയെ 2 കൊണ്ട്   നിശ്ശേഷം ഹരിക്കാം.
*ഒരു സംഖ്യയുടെ അക്കങ്ങളുടെ തുക ..................

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പ്രായം 
*   അച്ഛന്റെ/അമ്മയുടെ വയസ്സ് y വർഷം മുമ്പ് 
കന്റെ/മകളുടെ വയസ്സിന്റെ t1 ഇരട്ടിയായിരുന്നു.  ഇപ്പോൾ 12 ഇരട്ടി ആയാൽ മകന്റെ/മകളുടെ ഇപ്പോഴത്തെ വയസ്സ്  [y(t1-1)]/[t1-t2] ആയിരിക്കു................

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ട്രെയിൻ വേഗം = ദൂരം /സമയം സമയം  = ദൂരം / വേഗം
*km/hr നെ  m/s ലേക്ക് മാറ്റാൻ 5/18 കൊണ്ട് ഗുണിക്കുക.

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സമയവും ദൂരവും (Time & Distance ) ഒരു വസ്തതു ഒരു യൂണിറ്റ് സമയത്തിൽ സഞ്ചരിക്കുന്ന ദൂരത്തെയാണ് വേഗത എന്നു പറയുന്നത്.  
*ഒരു കാർ 1 മണിക്കുറിൽ 22 കിലോമീറ്റർ ദൂരം സഞ്ച രിക്കുന്നുവെങ്കിൽ ആ കാറ................

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കലണ്ടർ 
* ഒരു മാസത്തിലെ ഏതെങ്കിലും തിയ്യതിയോടു 7 കൂട്ടുകയോ കുറയ്ക്കുകയോ ചെയ്താൽ അതെ ദിവസം തന്നെ കിട്ടും 
ഉദാ: മാർച്ച് 1 തിങ്കൾ ആണെങ്കിൽ മാർച്ച്  8, 15,
22. 29 എന്നീ തീയതികൾ ................

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ക്ലോക്ക്  1.ഒരു ക്ലോക്കിലെ മണിക്കൂർ  സൂചി ഒരു മണിക്കുറിൽ എത്ര ഡിഗ്രി തിരിയും? (a)60    (b)5°  (c)30° (d)15°  ക്ലോക്കിന്റെ ഡയൽ ഒരു വൃത്തമാണ്. വൃത്തത്തിന്റെ ഡിഗ്രി അളവ് 360° ആണ്. ക്................

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പലിശ  സാധാരണ പലിശ കണക്കാക്കുന്നതിനുള്ള സൂത്രവാക്ക്യം I = PNR ഇവിടെ 'I' പലിശയെയും 'P' മുതലിനെയും 'N' വർഷത്തെയും 'R' പലിശ നിരക്കിനെയും കാണിക്കുന്നു. ശതമാനത്തിൽ തന്നിരിക്കുന്ന നിരക്കിനെ /100 ചേർ................

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കൃത്യങ്കങ്ങൾ  am x an  = amn a-n = 1/an (am)n = amn am/an = am-n am = an    m=n (a\b)n = an/bn a0 = 1, a ≠ 0 ഉദാ: 1) (32)3/5 x (64)-1/6 x (8)-1/3 എത്ര? (LDC Kottayam 2014) a) 8  b) 1   c) 16  d) 2 (32)3/5  = [(32)1/5]3  = 23 = 8 (64)-1/6 = [(64)1/6]-1 = 2-1 (8)-1/3    = [(8)1/3]-1    = 2-1 (32)3/5 x (64)-1/6 x (8)-1/3 = 8................

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സമയവും ദൂരവും 
*വേഗത = ദൂരം/സമയം

*സമയം = ദൂരം/വേഗത

*ദൂരം = വേഗത x സമയം

*km/hr നെ m/sec ആക്കാൻ 5/18 കൊണ്ട് ഗുണിക്കണം

*m/sec നെ km/hr ആക്കാൻ 18/5 കൊണ്ട് ഗുണിക്കണം

*m/min നെ km/hr ആക്കാൻ 3/50 കൊണ്ട് ഗുണിക്കണം

................

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സമയവും പ്രവൃത്തിയും
*A ഒരു ജോലി x ദിവസങ്ങൾ കൊണ്ടും B അതേ ജോലി y ദിവസം കൊണ്ടും ചെയ്താൽ രണ്ടുപേരും ചേർന്ന് xy\xy ദിവസം കൊണ്ട് ചെയ്ത് തീർക്കും.

*M1 ആളുകൾ D1 ദിവസം കൊണ്ട് പൂർത്തിയാക്കു................

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വിസ്തീർണ്ണവും വ്യാപ്തിയും 
*ഒരു ചതുരത്തിന്റെ നീളം "l" യൂണിറ്റും വീതി "b" യൂണിറ്റും ആയാൽ വിസ്തീർണ്ണം: l x b 
ചുറ്റളവ് : 2 (lb)
*ഒരു സമചതുരത്തിൻറെ വശം "a" യൂണിറ്റായാൽ വിസ്................

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ക്ലോക്ക്:
*ക്ലോക്കിലെ മിനിറ്റ് സൂചി ഒരു മിനിറ്റ് നീങ്ങുമ്പോൾ 6 ഡിഗ്രി വ്യത്യാസപ്പെടുന്നു. എന്നാൽ മണിക്കൂർ സൂചി "അര ഡിഗ്രി" വ്യത്യാസം മാത്രമാണ് ഉണ്ടാക്കുന്നത്.

*ഒരു ക്ലോക്ക................

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കലണ്ടർ: 
*സാധാരണ വർഷങ്ങളിൽ 52 ആഴ്ചയും ഒരു അധിക ദിവസവും ഉണ്ടാകും. ഒരു സാധാരണ വർഷത്തിൽ ആദ്യ ദിവസവും അവസാന ദിവസവും ഒരേ ദിവസമായിരിക്കും.

*അധിവർഷങ്ങളിൽ ആദ്യ ദിവസവും അവസാന ദിവസവും തമ്മിൽ ................

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വിസ്‌തീർണവും   വ്യാപ്‌തവും (Area & Volume) വിസ്‌തീർണവും (i)ഒരു ചതുരത്തിന്റെ നീളം 'I' യൂണിറ്റും വീതി 'b' യൂണിറ്റുമായാൽ വിസ്തീർണം =1&b  ചുറ്റളവ് =2 (Ib) വികർണം = 1^2  b^2 (ii)ഒരു സമചതുരത്ത................

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കൃത്യങ്കങ്ങൾ (Exponents)
*ആവർത്തനഗുണിതത്തെ ലളിതമാക്കുന്ന രീതിയാണ് കൃത്യങ്കങ്ങളിൽ ഉൾപ്പെടുന്നത്. ഉദാഹരണമായി 2x 2 x 2 x 2= 2^4 ഇതിൽ 4 നെ 2 ന്റെ കൃതി എന്നു പറയുന്നു.  പ്രധാന കൃത്യങ്ക നിയമങ്ങൾ [................

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പലിശ (Interest)
*നിക്ഷേപിച്ച പണം തിരിച്ചെടുക്കുമ്പോഴോ കടം വാങ്ങിയ തുക  തിരിച്ചുടുക്കുമ്പോഴോ പണത്തിനു പ്രതിഫലമായി നൽകപ്പെടുന്ന അധിക തുകയാണ് പലിശ 
മുതൽ (Principal) ഒരു ................

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ലാഭവും നഷ്ടവും (Profit & Loss) (i)ലാഭം (Profit) = വിറ്റവില (selling Price) - വാങ്ങിയവില (Cost  Price) (ii)നഷ്ടം = വാങ്ങിയവില - വിറ്റവില (iii)ലാഭം % = ലാഭം
*100/വാങ്ങിയവില
(iv)നഷ്ടം % = നഷ്ടം
*100/വാങ്ങിയവില
(v)വിറ്റവില = (100ലാ................

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ശരാശരി (Average) രണ്ടോ അതിലധികോ സംഖ്യകളുടെ തുകയെ ആ സംഖ്യകളുടെ എണ്ണം കൊണ്ടു ഹരിച്ചാൽ കിട്ടുന്ന ഹരണ ഫലമാണ് ആ സംഖ്യകളുടെ ശരാശരി.
*ശരാശരി = തുക / എണ്ണം 

* തുക = ശരാശരി
* എണ്ണം 

*എണ്ണ................

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സമയവും  പ്രവൃത്തിയും (Time & Work)
1.’A’ഒരു ജോലി ‘x’ ദിവസം കൊണ്ടും ‘B’അത് ‘y’ ദിവസം കൊണ്ടും ചെയ്താൽ രണ്ടും പേരും ചേർന്ന്   
xy/x  y  ദിവസം കൊണ്ട് ചെയ്തു തീർക്കും.
2.M1 ആളുകൾ D1 ദിവസം കൊണ്ട് പൂ................

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ജ്യാമിതി 
Ans: ചതുരം 
പരപ്പളവ് = നീളം x വീതി  ചുറ്റളവ് =2 (നീളം വീതി)                                                                                                                              
Ans: സമചതുരം 
പരപ്പള................

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ജോലിയും സമയവും 
*  A ഒരു ജോലി 'n' ദിവസം കൊണ്ട് ചെയ്യുമെങ്കിൽ
Aയുടെ ഒരു ദിവസത്തെ ജോലി 1/n ആയിരിക്കും.
* Aയുടെ ഒരു ദിവസത്തെ ജോലി 1/n ആണെങ്കിൽ
 A ആ ജോലി n ദിവസം കൊണ്ട് തീർക്കും. ഉദാ :[................

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ട്രെയിൻ  വേഗം= സഞ്ചരിച്ച ദൂരം സഞ്ചരിക്കാനെടുത്ത സമയ സഞ്ചരിച്ച ദൂരം സമയം = സഞ്ചരിച്ച ദൂരം                                 വേഗം =സഞ്ചരിച്ച ദൂരം= വേഗം X സമയം ഒരു ട്രെയിൻ ഒരുപോസ്റ്റ................

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പൈതഗോറസ് സിദ്ധാന്തം     2ഒരു മട്ടത്രികോണത്തിലെ നീളം കൂടിയ വശത്തിന്റെ (കർണം) വർഗം എന്നത് മറ്റ് രണ്ട് വശങ്ങളുടെ വർഗങ്ങളുടെ തുകയ്ക്ക് തുല്യമാണ് കർണം=പാദംലംബം AC= AB  BC AC=AB BC ................

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കുടുംബ ബന്ധങ്ങൾ  ജീവിതത്തിലെ  കുടുംബബന്ധങ്ങളെ ആധാരമാക്കിയാണ് ഈ വിഭാഗത്തിലെ ചോദ്യങ്ങൾ. താഴെ പറയുന്ന ബന്ധങ്ങൾ മനസ്സിലാക്കിയാൽ വളരെ വേഗം ഉത്തരം കണ്ടെത്താൻ കഴിയും.
* അച്ഛന്................

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മാതൃകാ ചോദ്യങ്ങൾ 1).  8 വർഷം മുമ്പ് അമ്മയുടെ വയസ്സ് മകളുടെ വയസ്സിന്റെ 10 മടങ്ങായിരുന്നു. ഇപ്പോൾ 4 മടങ്ങാണെങ്കിൽ  അമ്മയുടെ ഇപ്പോഴത്തെ വയസ്സ് എത്ര?  (a)46    (b)48  (c)50    (d)52 (2). 5 വർഷം ................

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സംഖ്യാശ്രേണികൾ (Number Series) ഏതെങ്കിലും നിയമമനുസരിച്ച് ഒന്നാമത്തേത്, രണ്ടാമത്തേത്, മൂന്നാമത്തേത് എന്നിങ്ങനെ ക്രമമായി എഴുതുന്ന ഒരു കൂട്ടം സംഖ്യകളാണ് സംഖ്യാ ശ്രേണികൾ.   ശ്രേണിയ................

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കോഡിങ് ഡികോഡിങ്  അക്കങ്ങളുടെയും അക്ഷരങ്ങളുടെയും പ്രത്യേക തരത്തിലുള്ള  ക്രമീകരണങ്ങളിലൂടെ രഹസ്യഭാഷ സൃഷ്ടിക്കുന്നതാണ് കോഡിങ്. രഹസ്യഭാഷയിൽ നിന്ന്കോഡ് ചെയ്ത അതേ രീതിയിൽ വിവ................

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പ്രോബബിലിറ്റി 
1. ഒരു ചെപ്പിൽ പത്ത് മുത്തുകളുണ്ട്. 6 എണ്ണം കറുത്തതും 4 എണ്ണം വെളുത്തതും. ഇതിൽ നിന്ന് കണ്ണടച്ച് ഒരു മുത്തെടുത്താൽ അത് കറുത്തത് ആകാനുള്ള സാധ്യത എത്ര?
(a)1/5 (b)2/5

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മാതൃകാ ചോദ്യങ്ങൾ 1). 12 സംഖ്യകളുടെ ശരാശരി 30 ആയാൽ 17 എന്ന സംഖ്യകൂടി ചേർത്താൽ പുതിയ ശരാശരി  (a) 28    (b)31  (c) 29    (d)32 2). 30 പേരുള്ള ഒരു സംഘത്തിന്റെ ശരാശരി 42 kg, പുതുതായി ഒരാൾ വന്നപ്പോൾ ശരാശരി................

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ശരാശരി സംഖ്യകളുടെ തുകയെ എണ്ണംകൊണ്ട് ഹരിക്കുമ്പോൾ ലഭിക്കുന്ന സംഖ്യയാണ് അവയുടെ ശരാശരി. ശരാശരി=സംഖ്യകളുടെ തുക /സംഖ്യകളുടെ എണ്ണം സംഖ്യകളുടെ തുക= ശരാശരിXസംഖ്യകളുടെ എണ്ണം................

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മാതൃകാ ചോദ്യങ്ങൾ
1. ഒരു വ്യാപാരി ഒരു സാരി 800 രൂപയ്ക്ക് വാങ്ങി 920 രൂപക്ക്  വിൽക്കുന്നു. ലാഭശതമാനം എത്ര ? 
(a) 10%    (b) 15%  (c) 18%    (d) 20%  ലാഭം %= (ലാഭം/വാങ്ങിയ വില) x 100% =(120/800) x 100% =120/8%=15% ഉത്ത................

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ലാഭം നഷ്ടം 
* ലാഭം %= (ലാഭം/വാങ്ങിയ വില) x 100%

* നഷ്ടം %= (നഷ്ടം/വാങ്ങിയ വില) x 100%

* ഡിസ്‌കൗണ്ട്%=(ഡിസ്‌കൗണ്ട് / പരസ്യവില) X100%

*  X സാധനങ്ങളുടെ വാങ്ങിയ വില Y സാധനങ്ങളുടെ
വിറ്റവിലയ്ക്ക................

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മാതൃകാ ചോദ്യങ്ങൾ 1, 1000 രൂപയ്ക്ക് ഒരു വർഷം 70 രൂപയാണ് പലിശയെ ങ്കിൽ പലിശനിരക്ക് എത്ര ശതമാനം? (a)5%    (b)6%  (c )7%      (d)8% 
2. 8% സാധാരണ പലിശ നിരക്കിൽ 5000 രൂപ  ബാങ്കിൽ നിന്ന് വായ്‌പ്പയെടുത്താ................

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പലിശ പലിശ പ്രധാനമായും രണ്ടു തരത്തിലുണ്ട്.
1. സാധാരണ പലിശ

2. കൂട്ടുപലിശ 
സാധാരണ പലിശ ഒരു നിശ്ചിത കാലാവധിയിൽ മുതലിന് നൽകേണ്ടി വരുന്ന പലിശ, സാധാരണ പലിശ കണക്ക................

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മാതൃകാ ചോദ്യങ്ങൾ SET-1 
1. 6000 രൂപ xy എന്നിവർക്കായി 2:8 എന്ന അംശബന്ധത്തിൽ വിഭജിച്ചാൽ x ന് എത്ര രൂപ ലഭിക്കും? 
 (a) 2000     (b)2400  (c)3000      (d)3600 
2. ഒരു സഞ്ചിയിൽ 5 രൂപ, 2 രൂപ, 1 രൂപ, 50 പൈസ, 25 പൈ................

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അംശ ബന്ധവും അനുപാതവും  ഒരേ യൂണിറ്റിലുള്ള അളവുകൾ തമ്മിലുള്ള ബന്ധത്തെ സൂചിപ്പിയ്ക്കുന്നതാണ് അംശബന്ധം, രണ്ടാമത്തേത് ആദ്യത്തേതിൽ എത്ര പ്രാവശ്യം ഉൾക്കൊണ്ടിട്ടുണ്ട് എന്ന് കാ................

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മാതൃകാ ചോദ്യങ്ങൾ .
1. ഒരാളിന്റെ വേതനം 20% കുറച്ച ശേഷം 20% വർധിപ്പിച്ചാൽ ഉണ്ടാകുന്ന മാറ്റം 
(a) 4% ലാഭം       (b) 4%നഷ്ടം  (c) 5% നഷ്ടം       (d) വ്യത്യാസമില്ല
2. ഒരു പരീക്ഷയിൽ 40% വിദ്യാർഥികൾ കണക................

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ശതമാനം 
*  X % എന്നാൽ  X/100 എന്നർത്ഥം

* ഭിന്ന സംഖ്യയെയും ദശാംശ സംഖ്യയെയും ശതമാനമാക്കാൻ 100 കൊണ്ട് ഗുണിച്ചാൽ മതി 
ഉദാ:1/2 x 100=50%.
0.35x100=35%

*  ശതമാന സംഖ്യയെ  ഭിന്നസംഖ്യയാക്കി മാറ്റാൻ 100

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കൃത്യങ്കങ്ങൾ, കരണികൾ ആവർത്തിച്ചുവരുന്ന ഗുണനക്രിയ ചുരുക്കി.എഴുതുന്ന രീതിയാണ് കൃത്യങ്കങ്ങൾ. 4x4x4x4×4=4^5 a^3=a×a×a ഇതിൽ a എന്ന സംഖ്യയെ 'പാദം' എന്നും 3 എന്ന സംഖ്യയെ 'കൃതി' എന്നും പറയുന്നു. ക................

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ഭിന്നസംഖ്യകൾ ഒന്നിനെ തുല്യമായ 7    ഭാഗങ്ങളാക്കി അതിൽ 3 ഭാഗം സൂചിപ്പിക്കാൻ 3/7എന്ന് പറയുന്നു.  a/b എന്ന ഭിന്ന സംഖ്യയിൽ 'a'യെ അംശം എന്നും 'b'യെ ഛേദം എന്നും പറയുന്നു  ഒരു  ഭിന്നസംഖ്യയിലെ അംശ................
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