Problem 1 :
Divide 300 by 7, list out dividend, divisor, quotient, remainder and write division algorithm.
Problem 2 :
Divide 258 by 9, list out dividend, divisor, quotient, remainder and write division algorithm.
Problem 3 :
Divide 400 by 8, list out dividend, divisor, quotient, remainder and write division algorithm.
Problem 4 :
Divide 1675 by 13, list out dividend, divisor, quotient, remainder and write division algorithm.
Problem 5 :
What is dividend, when divisor is 17, the quotient is 9 and the remainder is 5 ?
Problem 6 :
When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
Problem 7 :
On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor ?
Problem 8 :
On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder ?
Problem 1 :
Divide 300 by 7, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution :
Let us divide 300 by 7 using long division as given below.
From the above long division, we have
Dividend = 300
Divisor = 7
Quotient = 42
Remainder = 6
Division algorithm for the above division :
Problem 2 :
Divide 258 by 9, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution :
As we have seen in problem 1, if we divide 258 by 9 using long division, we get
Dividend = 258
Divisor = 9
Quotient = 28
Remainder = 6
Division algorithm for the above division is
258 = 28x9 + 6
Problem 3 :
Divide 400 by 8, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution :
As we have seen in problem 1, if we divide 400 by 8 using long division, we get
Dividend = 400
Divisor = 8
Quotient = 50
Remainder = 0
Division algorithm for the above division is
400 = 50x8 + 0
Problem 4 :
Divide 1675 by 13, list out dividend, divisor, quotient, remainder and write division algorithm.
Solution :
As we have seen in problem 1, if we divide 1675 by 13 using long division, we get
Dividend = 1675
Divisor = 13
Quotient = 128
Remainder = 11
Division algorithm for the above division is
1675 = 128x13 + 11
Problem 5 :
What is dividend, when divisor is 17, the quotient is 9 and the remainder is 5 ?
Solution :
Using division algorithm
Dividend = Divisor x quotient + Remainder
Dividend = 17 x 9 + 5
Dividend = 153 + 5
Dividend = 158
So, the dividend is 158.
Problem 6 :
When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
Solution :
Using division algorithm
Dividend = Divisor x quotient + Remainder
From the given information, we have
n = 8q + 3
To find the remainder, when 6n is divided by 8, we multiply 6 on both sides.
6n = 48q + 18
6n = 48q + 16 + 2
Factoring out 8 from 48 and 16, we get
6n = 8(6q + 2) + 2
8(6q + 2) is the multiple of 8 and remainder is 2.
So, we get 2 as remainder when dividing 6n by 8.
Problem 7 :
On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor ?
Solution :
Let x be the divisor.
Dividend = 12401, divisor = x, quotient = 76 and remainder = 13.
12401 = 76x + 13
12401 - 13 = 76x
Solving for x, we get the divisor.
76x = 12388
x = 12388/76
x = 163
So, the divisor is 163.
Problem 8 :
On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder ?
Solution :
Let x be the quotient on dividing a number by 342, which yields the remainder 47.
By applying the above information in division algorithm, we get
Number = 342x + 47
Now, we should divide the same number by 18 and find the remainder.
Representing 342x + 47 as the multiple of 18, we get
342x + 47 = (18 ⋅ 19x) + 36 + 11
342x + 47 = (18 ⋅ 19x) + 2 ⋅ 18 + 11
Factoring out 18, we get
342x + 47 = 18(19x + 2) + 11
18(19x + 2) is the multiple of 18.
So, the remainder is 11.
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