Question

Q) write remainders on dividing the counting number from 1 to 10 by 3?
a) what is the sum of the remainders?
b) what is the sum of the remainders on dividing the numbers from 1 to 10 by 4?
c) what is the sum of the remainders on dividing numbers from 1 to 100 by 3?​

Answer 1

Given:

The numbers 3 and 4.

To find:

Write remainders on dividing the counting number from 1 to 10 by 3?

a) what is the sum of the remainders?

b) what is the sum of the remainders on dividing the numbers from 1 to 10 by 4?

c) what is the sum of the remainders on dividing numbers from 1 to 100 by 3?​

Solution:

a) what is the sum of the remainders on dividing the numbers from 1 to 10 by 3?

1 ÷ 3 ⇒ remainder  = 1

2 ÷ 3 ⇒ remainder  = 2

3 ÷ 3 ⇒ remainder  = 0

4 ÷ 3 ⇒ remainder  = 1

5 ÷ 3 ⇒ remainder  = 2

6 ÷ 3 ⇒ remainder  = 0

7 ÷ 3 ⇒ remainder  = 1

8 ÷ 3 ⇒ remainder  = 2

9 ÷ 3 ⇒ remainder  = 0

10 ÷ 3 ⇒ remainder  = 1

The series is as follows: 1 2 0

(1 + 2 + 0) × 3 + 1 = 3 × 3 + 1 = 10

Therefore, the sum of remainder is 10

b) what is the sum of the remainders on dividing the numbers from 1 to 10 by 4?

1 ÷ 4 ⇒ remainder  = 1

2 ÷ 4 ⇒ remainder  = 2

3 ÷ 4 ⇒ remainder  = 3

4 ÷ 4 ⇒ remainder  = 0

5 ÷ 4 ⇒ remainder  = 1

6 ÷ 4 ⇒ remainder  = 2

7 ÷ 4 ⇒ remainder  = 3

8 ÷ 4 ⇒ remainder  = 0

9 ÷ 4 ⇒ remainder  = 1

10 ÷ 4 ⇒ remainder  = 2

The series is as follows: 1 2 3 0

(1 + 2 + 3 + 0) × 2 + 1 + 2 = 6 × 2 + 3 = 15

Therefore, the sum of remainder is 15

c) what is the sum of the remainders on dividing numbers from 1 to 100 by 3?​

Consider (a) for this solutions:

The series is as follows: 1 2 0

(1 + 2 + 0) × 33 + 1 = 3 × 33 + 1 = 100

Therefore, the sum of remainder is 100