## NCERT Exercise 3.3 Solution Part-4 class six math

In this section question number 4 to 6 of NCERT Exercise 3.3 have been solved. Numbers given in question number 4 are to be tested for divisibility by 11. In question number 5 two numbers have been given in which one digit in each number is missing. The missing number is to be filled in such a way that given numbers will become divisible by 3. In question number 6 two numbers, each with a missing digit, are given. The missing digit is to be identified so that the numbers will become divisible by 11.

Question (4) Using divisibility tests, determine which of the following numbers are divisible by 11:

(a) 5445

**Answer**

**Divisible by 11: Yes**

17852 ÷ 11 = 495

**Explanation**

The difference between the sum of digits at even places and at odd places of 5445 counting from right is equal to zero, thus 5445 is divisible by 11.

= 5 + 4 – (5 + 4)

= 9 – 9 = 0

Thus, 5445 is divisible by 11

17852 ÷ 11 = 495

(b) 10824

**Answer**

**Divisible by 11: Yes**

10824 ÷ 11 = 984

**Explanation**

The difference between the sum of digits at even places and at odd places of 10824 counting from right is equal to eleven (11), thus 10824 is divisible by 11.

= 4 + 8 + 1 – (2 + 0)

= 13 – 2 = 11

Thus, 10824 is divisible by 11

10824 ÷ 11 = 984

(c) 7138965

**Answer**

**Divisible by 11: No**

**Explanation**

The difference between the sum of digits at even places and at odd places of 7138965 counting from right is neither equal to eleven (11) or zero (0), thus 7138965 is not divisible by 11.

= 5 + 9 + 3 + 7 – (6 + 8 + 1)

= 24 – 15 = 9

Thus, 7138965 is not divisible by 11

(d) 70169308

**Answer**

**Divisible by 11: Yes**

70169308 ÷ 11 = 6379028

**Explanation**

The difference between the sum of digits at even places and at odd places of 70169308 counting from right is equal to zero (0), thus 70169308 is divisible by 11.

= 8 + 3 + 6 + 0 – (0 + 9 + 1 + 7)

= 17 – 17 = 0

Thus, 70169308 is divisible by 11

70169308 ÷ 11 = 6379028

(e) 10000001

**Answer**

**Divisible by 11: Yes**

10000001 ÷ 11 = 909091

**Explanation**

The difference between the sum of digits at even places and at odd places of 10000001 counting from right is equal to zero (0), thus 10000001 is divisible by 11.

= 1 + 0 + 0 + 0 – (0 + 0 + 0 + 1)

= 1 – 1 = 0

Thus, 10000001 is divisible by 11

10000001 ÷ 11 = 909091

(f) 901153

**Answer**

**Divisible by 11: Yes**

901153 ÷ 11 = 91923

**Explanation**

The difference between the sum of digits at even places and at odd places of 901153 counting from right is equal to eleven (11), thus 901153 is divisible by 11.

= 5 + 1 + 9 – (3 + 1 + 0)

= 15 – 4 = 11

Thus, 901153 is divisible by 11

901153 ÷ 11 = 81923

Question (5) Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3:

(a) ___6724 (b) 4765__2

**Answer**

(a) ___6724

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3 also.

Thus, __ 2__ + 6 + 7 + 2 + 4 = 21

27624 ÷ 3 = 9208

Thus, the smallest number is **2** **Answer**

(b) 4765__2

4 + 7 + 6 + 5 + __ 6__ + 2 = 30

476562 ÷ 3 = 158854

Thus, the greatest number is **6** **Answer**

Thus, the smallest number for question (a) = 2 and greatest number for question (b) = 6 **Answer**

Question (6) Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11:

(a) 92 ____ 389 (b) 8 __ 9484

**Solution**

If the difference between the sum of digits situated at odd and even places counting from right of a number is either equal to zero (0) or eleven (11), then the number is divisible by 11.

Thus, **Answer** (a) 92 ____ 389

The sum of digits situated at odd places counting from right

= 9 + 3 + 2 = 14

And, the sum of digits situated at even places counting from right

= 8 + __ + 9

= ___ + 17

Now, 17 – 14 = 3

Here, 11 – 3 = 8

This means if we add 8 to the 3, then it will become 11

Thus, 8 + ** 8** + 9 = 25

Now, 25 – 14 = 11

This, means if 8 is in blank space then, the given number will be divisible by 11.

Thus, the number is 92** 8**389

92** 8**389 ÷ 3 = 84399

Thus, the missing number = 8 **Answer**

**Answer** (b) 8 __ 9484

The sum of digits situated at odd places counting from right

= 4 + 4 + __ = 8 + __

And, the sum of digits situated at even places counting from right

= 8 + 9 + 8 = 25

Now, 25 – 11 = 14

Thus, missing digit = 14 – 8 = 6

Now, the sum of digits situated at odd places counting from right

= 4 + 4 + ** 6** = 14

And, the sum of digits situated at even places counting from right

= 8 + 9 + 8 = 25

Now, the difference between digits situated at odd and even places of the given number

= 25 – 14 = 11

Thus, 8** 6**9484 is divisible by 11

8** 6**9484 ÷ 3 = 79044

Thus, the missing number = 6 **Answer**