EXERCISE-3E
Question 1
Q.1. Divide and check your answer by the corresponding multiplication in each of the following :
(i) $1936 / 16$
(ii) 19881/47
(iii) 257796/341
(iv) 612846/582
(v) 34419/149
(vi) $39039 / 1001$
Ans.
<to be added>
Question 2
(i) $6971 / 47$
(ii) $4178 / 35$
(iii) $36195 / 153$
(iv) 93575/400
(v) $23025 / 1000$
(vi) 16135/875
<to be added>
Question 3
Q.3. Find the value of :
(i) $65007 / 1$
(ii) $0 / 879$
(iii) 981 + 5720/10
(iv) $1507-625 / 25$
(v) 32277/(648 - 39)
(vi) 1573/1573 - 1573/1573
Ans.
(i) We know that any number (non-zero) divided by 1 gives the number itself
$\therefore 65007 / 1=65007$
(ii) We know that 0 divided by any natural number gives 0
$\begin{aligned}
& \therefore 0 / 879=0 \\
& \text { (iii) } 981+5720 / 10=981+(5720 / 10) \\
& =981+572 \\
& =1553
\end{aligned}$
$\begin{aligned}
& \text { (iv) } 1507-62525=1507-(62525) \\
& =1507-25 \\
& =1482
\end{aligned}$
(v) <to be added>
$\begin{aligned} & \text { (vi) } 1573 / 1573-1573 / 1573 \\ & =(1573 / 1573)-(1573 / 1573) \\ & =1-1=0\end{aligned}$
Question 4
Q.4. Find a whole number $n$ such that $n / n=n$.
Ans. We have $\mathrm{n} / \mathrm{n}=\mathrm{n}$
let $n=1,1 / 1=1$
$1=1$
which is true
Hence 1 is the required whole number.
Question 5
Q.5. The product of two numbers is 504347 . If one of the numbers is 317 , find the other.
Question 6
Q.6. On dividing 59761 by a certain number, the quotient is 189 and the remainder is 37 . Find the divisor.
Ans.
Here Dividend = 59761, Quotient $=189$
Remainder $=37$
We know that Dividend = Divisor $\times$ Quotient + Remainder
$\therefore 59761=$ Divisor $\times 189+37$
59761 - 37 = Divisor $\times 189$
59724 = Divisor $\times 189$
Divisor $\times 189=59724$
Divisor $=59724 / 189$
<division to be added>
$\therefore$ Divisor $=59724 / 189=316$
Question 7
Q.7. On dividing 55390 by 299 , the remainder is 75 . Find the quotient, using the division algorithm.
Ans.
Here dividend $=55390$,
Divisor $=299$ and Remainder $=75$
By division algorithm, we have
Dividend $=$ Quotient $\times$ Divisor + Remainder
$\therefore 55390=$ Quotient $\times 299+75$
55390 - 75 = Quotient × 299
55315 = Quotient $\times 299$
Quotient $\times 299=55315$
$\therefore$ Quotient $=55315 / 299$
<division to be added>
$\therefore$ Required quotient $=185$
Question 8
Q.8. What least number must be subtracted from 13601 to get a number exactly divisible by 87 ?
Ans.
On dividing 13601 by 87 , we have
<division to be added>
It is clear that if we subtract 29 from 13601 , the resulting number will be exactly divisible by 87.
$\therefore$ The required least number $=29$.
Question 9
Question 10
Q.10. Find the largest 4-digit number divisible by 16 .
Ans.
Greatest 4-digit number $=9999$
<division to be added>
On, dividing by 16 , we get remainder as 15
$\therefore$ The required largest 4-digit number
$=9999-15=9984$
Question 11
Q.11. Divide the largest 5-digit number by 653. Check your answer by the division algorithm.
Ans. Largest number of 5-digits $=99999$
On dividing 99999 by 653 , we have
<division to be added>
$\therefore$ Quotient $=153$, Remainder $=90$
Check : By division algorithm
$\begin{aligned} & \text { Dividend }=\text { Divisor } \times \text { Quotient }+ \text { Remainder } \\ & =653 \times 153+90 \\ & =99909+90 \\ & =99999\end{aligned}$
Question 12
Q.12. Find the least 6-digit number exactly divisible by 83 .
Ans. The least 6-digit number $=100000$
On dividing 100000 by 83 , we have
<division to be added>
It is clear that if we add 15 to 68 , it will become 83 which is divisible by 83 .
$\therefore$ Required least 6-digit number
$=100000+15=100015$
Question 13
Q.13. 1 dozen bananas cost Rs. 29. How many dozens can be purchased for Rs. 1392 ?
Ans. Cost of 1 dozen bananas $=$ Rs. 29
$\therefore$ Bananas can be purchase in Rs. 1392
<division to be added>
$\text { = 1392/29 = } 48 \text { dozens }$
Question 14
Q.14. 19625 trees have been equally planted in 157 rows. Find the number of trees in each row.
Ans. Total number of trees $=19625$
Total number of rows $=157$
$\therefore$ Number of trees in each row
$=19625 / 157$
<division to be added>
$\therefore$ Number of trees in each row $=125$
Question 15
Q.15. The population of a town is 517530 . If one out of every 15 is reported to be literate, find how many literate persons are there in the town.
Ans. Total population of the town $=517530$ Since there is one educated person out of 15 .
$\therefore$ Total number of educated persons in the town $=517530 / 15$
<division to be added>
$\therefore$ Total number of educated persons in the town $=34502$.
Question 16
Q.16. The cost price of 23 colour television sets is Rs. 570055 . Determine the cost price of each TV set if each costs the same.
Ans.
Cost of 23 colour TV sets = Rs. 570055
Cost of 1 colour TV set
<division to be added>
$\begin{aligned} & \therefore \text { Cost of } 1 \text { colour TV set } \\ & =\text { Rs. } 570055 / 23=\text { Rs. } 24785\end{aligned}$
Question 4
Q.4. Find a whole number $n$ such that $n / n=n$.
Ans. We have $\mathrm{n} / \mathrm{n}=\mathrm{n}$
let $n=1,1 / 1=1$
$1=1$
which is true
Hence 1 is the required whole number.
Question 5
Ans. Product of two numbers $=504347$
One number $=317$
$\therefore$ Other number $=504347 / 317$
<division to be added>
$\therefore$ Other number $=1591$
Question 6
Ans.
Here Dividend = 59761, Quotient $=189$
Remainder $=37$
We know that Dividend = Divisor $\times$ Quotient + Remainder
$\therefore 59761=$ Divisor $\times 189+37$
59761 - 37 = Divisor $\times 189$
59724 = Divisor $\times 189$
Divisor $\times 189=59724$
Divisor $=59724 / 189$
<division to be added>
$\therefore$ Divisor $=59724 / 189=316$
Question 7
Q.7. On dividing 55390 by 299 , the remainder is 75 . Find the quotient, using the division algorithm.
Ans.
Here dividend $=55390$,
Divisor $=299$ and Remainder $=75$
By division algorithm, we have
Dividend $=$ Quotient $\times$ Divisor + Remainder
$\therefore 55390=$ Quotient $\times 299+75$
55390 - 75 = Quotient × 299
55315 = Quotient $\times 299$
Quotient $\times 299=55315$
$\therefore$ Quotient $=55315 / 299$
<division to be added>
$\therefore$ Required quotient $=185$
Question 8
Ans.
On dividing 13601 by 87 , we have
<division to be added>
It is clear that if we subtract 29 from 13601 , the resulting number will be exactly divisible by 87.
$\therefore$ The required least number $=29$.
Question 9
Q.9. What least number must be added to 1056 to get a number exactly divisible by 23 ?
Ans.
Here dividend $=1056$, Divisor $=23$
By actual divison, we have
<division to be added>
It is clear that if we add 2 to 21 , it will become 23 which is divisible by 23.
$\therefore$ Required least number $=2$.
Question 10
Ans.
Greatest 4-digit number $=9999$
<division to be added>
On, dividing by 16 , we get remainder as 15
$\therefore$ The required largest 4-digit number
$=9999-15=9984$
Question 11
Q.11. Divide the largest 5-digit number by 653. Check your answer by the division algorithm.
Ans. Largest number of 5-digits $=99999$
On dividing 99999 by 653 , we have
<division to be added>
$\therefore$ Quotient $=153$, Remainder $=90$
Check : By division algorithm
$\begin{aligned} & \text { Dividend }=\text { Divisor } \times \text { Quotient }+ \text { Remainder } \\ & =653 \times 153+90 \\ & =99909+90 \\ & =99999\end{aligned}$
Question 12
Ans. The least 6-digit number $=100000$
On dividing 100000 by 83 , we have
<division to be added>
It is clear that if we add 15 to 68 , it will become 83 which is divisible by 83 .
$\therefore$ Required least 6-digit number
$=100000+15=100015$
Question 13
Ans. Cost of 1 dozen bananas $=$ Rs. 29
$\therefore$ Bananas can be purchase in Rs. 1392
<division to be added>
$\text { = 1392/29 = } 48 \text { dozens }$
Question 14
Q.14. 19625 trees have been equally planted in 157 rows. Find the number of trees in each row.
Ans. Total number of trees $=19625$
Total number of rows $=157$
$\therefore$ Number of trees in each row
$=19625 / 157$
<division to be added>
$\therefore$ Number of trees in each row $=125$
Question 15
Q.15. The population of a town is 517530 . If one out of every 15 is reported to be literate, find how many literate persons are there in the town.
Ans. Total population of the town $=517530$ Since there is one educated person out of 15 .
$\therefore$ Total number of educated persons in the town $=517530 / 15$
<division to be added>
$\therefore$ Total number of educated persons in the town $=34502$.
Question 16
Q.16. The cost price of 23 colour television sets is Rs. 570055 . Determine the cost price of each TV set if each costs the same.
Ans.
Cost of 23 colour TV sets = Rs. 570055
Cost of 1 colour TV set
<division to be added>
$\begin{aligned} & \therefore \text { Cost of } 1 \text { colour TV set } \\ & =\text { Rs. } 570055 / 23=\text { Rs. } 24785\end{aligned}$
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