Question

a number when divided by 72 leaves a reminder of 10. What will be the remainder when the same number is divided by 9?​

Answer 1

Given :

• Divisor I = 72
• Remainder = 10

To find :

• The remainder when the same number is divided by 9

Solution :

Let the number be x & the quotient be q

We know that,

• Number = Divisor x quotient + remainder
• x = 72 x q + 10
• x = 72q + 10
• x = (9 x 8)q + 10
• x = (9 x 8)q + 9 + 1
• x = 9(8q + 9 ) + 1

from the last expression,we get that when x gets divided by 9,yields a quotient of (8q+9) with a remainder of 1 .

Therefore,the remainder when the same number which when divided by 72 leaves a remainder of 10 ,gets divided by 9 would be 1 .

Answer 2

The remainder is 1.

Explanation:

When a number is divided by 72 and leaves a remainder of 10, we can express this as:

Number = 72n + 10, where n is the quotient of the division.

To find the remainder when the same number is divided by 9, we simply divide the expression for the number by 9:

(72n + 10) ÷ 9

To find the remainder, we need to find the value of this expression when divided by 9. The remainder is the value left after dividing as much as possible. Let's simplify the expression:

(72n + 10) ÷ 9 = (72n ÷ 9) + (10 ÷ 9)

The term (72n ÷ 9) is divisible by 9 because 72 is divisible by 9. So, it doesn't contribute to the remainder. The term (10 ÷ 9) is not divisible by 9, so it will include the remainder.

When we divide 10 by 9, we get 1 remainder 1. Therefore, the remainder when the same number is divided by 9 is 1.

To check this, let the number be 154 (so n = 2).

Divide 154 by 72 and by 9 and observe the remainders:

154 ÷ 72 = 2 remainder 10

154 ÷ 9 = 17 remainder 1

Hence, the remainder is 1 when the same number is divided by 9.