# DIVISION ALGORITHM WORKSHEET

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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