Important Mathematics question in division of fractions for CBSE class 9

Important Mathematics question in division of fractions for CBSE class 9

Important Mathematics question in division of fractions

In this post we will learn about division of fractions . Therefore in this post learn two chapters one is division and other is number system. Therefore In division have four components.

Dividend

Divisor

Quotients and

Remainder.


Dividend: – We denoted by a ,  and it is greater than from divisor.

Divisor: – We denoted by small letter b. It is smaller than from dividend.

Quotient: – We denoted from q . It is formation after operation of dividend and divisor.

Remainder:- It is a remainder and we  denoted by r.

In this article, we will learn to solve some questions based on factor, divisor. Which will be very useful for you?


Division on Numbers

If any number a is divided by the number b and quotient is q and remainder is r then,

a =bq + r , where 0 ≤ r < b
a = भाज्य (dividend )
b = भाजक ( divisor)
q = भागफल (quotient )
r = शेषफल (remainder )
भाज्य = ( भाजक x भागफल ) + शेषफल
a = ( b x q ) + r

division of fractions related some solved problems

Q1: Find out the divisor if dividend is 1043, quotient is 11 and remainder is 20 . (1043 को किसी संख्यां से भाग देने पर भागफल 11 तथा शेषफल 20 प्राप्त होता है, तो भाजक को ज्ञात करें|)
Solution:- We have dividend = 1043 , quotient = 11 and remainder = 20
we know that,
a = ( b x q ) + r
let the divisor is b then,
=> 1043 = ( b x 11 ) + 20
=> b = (1043 – 20)/11
=> b = 1023/11 = 93 Ans.

Q2:Which number should be subtracted to the smallest of among 1000 , that the remaining number be completely divisible by 19 ? (1000 में से छोटी से छोटी कौन-सी संख्यां को घटाई जाय, कि शेष बची संख्यां 19 से पूर्णतया विभक्त हो जाय ?)
Solve:- If we divide 1000 from 19 then we get divisor = 19 & remainder = 12 ans

division of fractions dividend divisor quotient remainder solved

Q3:If we dividing 195 by any number we get remainder 47. But if divide this number by 15 then how much remainder left ? (किसी संख्यां को 195 से भाग देने पर 47 शेष बचते है | अगर इस संख्यां को 15 से भाग दिया जाय तो कितना शेष बचेगा ?)
Solve:- First phase, We have , b = 195 , q = ? , r = 47
a = (b x q ) + r ( by formula)
=> a = 195 x q + 47
=> a = 15 x 13q + 15 x 3 + 2
=> a = 15 ( 13q + 3 ) + 2
Therefore, Remainder = 2 Ans.

Q4:Calculate the divisor if dividend is 10690 , quotient is 73 and remainder is 32. (10690 को किसी संख्यां से भाग देने पर भागफल 73 तथा शेषफल 32 प्राप्त होता है, भाजक कि गणना करें.)
Solve:- We have, dividend = 10690 , divisor = ? , Quotient = 73 , remainder = 32
Therefore,
=> dividend = ( divisor x quotient ) + remainder
=> divisor = ( dividend – remainder) ÷ quotient
= ( 10690 – 32 ) ÷ 73
= 10658/73 = 146

Q5: Which number should be subtracted to the smallest of among 3100 , that the remaining number be completely divisible by 17 ? (3100 में से कौन-सी छोटी से छोटी संख्यां घटाई जाय | कि शेष बची संख्यां 17 से पूर्णतया विभक्त हो )

Solve:- If we divide 3100 from 17 we get divisor = 182 an remainder = 6 ans

Q6:What is the nearest number to 4508 which is completely divisible by 21? (4508 के समीपतम कौन-सी संख्यां है जो 21 से पूर्णतया विभक्त हो )
Solve:- We know

Division of fractions mathematics for cbse class 9

dividend = ( divisor x quotient ) + remainder
= 4508 ÷ 21 = 214 + 14
= divisor = 214 & remainder = 14 ans

Q7: In an action of division, the quotient is 403, the divisor 100 and the remainder 58, then how much is the dividend.(भाग कि एक क्रिया में भागफल 403 , भाजक 100 तथा शेषफल 58 है तो भाज्य कितना है )
Solve: We have, divisor= 100 , quotient = 403, remainder= 58, dividend = ?
dividend = ( divisor x quotient ) + remainder
=> dividend = ( 100 x 403 ) + 58
= 40300 + 58 = 40358 Ans.

Q8:-By multiplying 48 by which number the multiplication obtained will be equal to the multiplication of 173 and 240.( 48 को किस संख्यां से गुना करने पर प्राप्त गुणनफल 173 तथा 240 के गुणनफल के बराबर होगा )
Solve:- Let that number is x
=> 48 x = 173 x 240
=> x = 41520/48 = 865 ans.

Q9:-What is the sum of all prime numbers between 50 and 90? (50 और 90 के बीच सभी अभाज्य संख्याओं का योग कितना है )
Solve:-The following number is = 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 = 635 ans

Q10:-Among 3428 which minimum numbers subtracted which number should be completely divisible by the number obtained 13.(3428 में से कौन-सी न्यूनतम संख्यां से घटाया जाय जो प्राप्त संख्यां 13 से पूर्णतया विभक्त हो जाय )
Solve:- That number is = 263 x 13 + 9 = 9 ans.

Dividend divisor quotient remainder related problems

Q11:-If we dividing 136 by any number we get remainder 36. But if divide this number by 17 then how much remainder left ? (किसी संख्यां को 136 से भाग देने पर शेषफल 36 प्राप्त होता है, अगर उसी संख्यां को 17 से भाग दे तो शेष कितना बचेगा ) Ans:- 2 (hint: same as Q No.3)

Q12:-If we divided 156 by any number we get remainder 29. But if divide this number by 13 then how much remainder left ?(किसी संख्यां को 156 से भाग देने पर शेषफल 29 शेष बचता है , उसी संख्यां को 13 से भाग देने पर क्या बचेगा)
Ans:- 3 (Hint: same as Q No.3)

Q13:-When a number divided by 195 then we get remainder is equal to 47. If divide the same number by 15 then how mauch remainder be left ? (किसी संख्यां को 195 से भाग देने पर 47 शेष बचता है | यदि उसी संख्यां को 15 से विभक्त करें तो कितना शेष बचेगा )
Solve: Ans: 2 (Hint: solve according to Q3)

Q14:-Which small number should be subtracted from 4000 so that the remaining number is completely divisible by 19.(4000 में से छोटी सी छोटी कौन-सी संख्यां घटाई जाय कि शेष बची संख्यां 19 से पूर्णतया विभक्त हो जाए )
Solve:- 10 (Hints:- solve according to Q No.5)

Q15:-What is the smallest 6-digit number? Which is completely divisible by 111.( छः अंकों की छोटी-सी छोटी संख्या कौन है ? जो 111 से पूर्णतया विभक्त हो)
Solve:- 6-digit smallest number = 100000
= 100000 + ( 111-100) = 100000 + 11 = 100011 ans

Q16:-The smallest number that is added to 803642 is a multiple of 11. Find that number.(वह छोटी सी छोटी संख्यां जिसे 803642 में जोड़ने पर प्राप्त संख्यां 11 की गुणज हो | वह संख्यां ज्ञात करें )

Dividend divisor quotient remainder worksheets

Solve:- If we divide 803642 from 11 we get = 73058 and remainder = 4
=>Number = 11 – 4 = 7 Ans.

Q17: What is the smallest three-digit number which is completely divisible by 14? ( तीन अंकों की छोटी सी छोटी संख्यां कौन-सी है जो 14 से पूर्णतया विभाजित हो)
Solve:- 112 (Hint: same as Q No.15)

Q18: Find the largest 5 digit number which is completely divisible by 463.(5 अंकों की वह बड़ी से बड़ी संख्यां ज्ञात करें जो 463 से पूर्णतः विभक्त हो )
Solve:-99545 (Hint: same as 15)

Q19: Find out the divisor if dividend is 7865321, quotient 33612 and remainder is 113. (7865321 को किस संख्यां से भाग दिया जाय तो भागफल 33612 तथा शेष 113 बचेगा | तो भाजक निकले)
Solve:- ans 234 ( same as Q No.4)

Q20: If any number is divideb by 6 then we get remainder is 3. But the square of the same number divided by 6 then what will be remainder?(किसी संख्यां को 6 से भाग देने पर शेष 3 बचता है|अगर उसी संख्यां के वर्ग को 6 से भाग दिया जय तो शेष कितना बचेगा )
Solve:- let to be the number = 6n + 3 , where n is integer
after squaring = (6n + 3 )2 = 36n2+36n+9 = 6(6n2+6n+1) +3 = 3 ans

Q21:-By dividing a number by 9,11,13 respectively get remainder 8,9 and 8. Bu if reverse the divisors then what wil the remainder?(किसी संख्यां को क्रमशः 9 , 11 , 13 से विभक्त करने पर क्रमशः 8 , 9 , 8 शेष बचता है | यदि विभाजकों के क्रम को उलट दिया जाय तो शेष क्या बचेगा )
Solve: 9 a 8
11 b 9
13 c 8

c= 13×1+8 = 21 b = 11 x 21+9 = 240 c = 9x 240 + 8 = 2168

13 2168 10
11 166 1
9 15 6

Therefore remainder = 10, 1 , 6

Division of fractions word problems

Q22:The four natural numbers are such that adding them three by three gives 180, 197, 208 and 222 respectively. So what will be the mean of these numbers? ( चार प्राकृत संख्याएँ इस प्रकार है उन्हें तीन तीन करके जोड़ने पर क्रमशः 180 , 197 , 208 और 222 प्राप्त होता है| तो इन संख्याओं का माध्य क्या होगा )
Solve:- Let the natural number is a , b , c and d
=> a + b + c = 180 , b + c + d = 197 , c + d + a = 208 and d + a + b = 222
By adding
=> 3 ( a + b + c + d ) = 807
=> a + b + c + d = 807/3 = 269
=> Mean = 269/4 Ans

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