Rd Sharma 2018 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Question 1:

Given that the number $\overline{35\alpha 64}$ is divisible by 3, where α is a digit, what are the possible values of α?

Question 2:

If x is a digit such that the number $\overline{18x71}$ is divisible by 3, find possible values of x.

Question 3:

If x is a digit of the number $\overline{66784x}$ such that it is divisible by 9, find possible values of x.

Question 4:

Given that the number $\overline{67y19}$ is divisible by 9, where y is a digit, what are the possible values of y?

Question 5:

If $\overline{3x2}$ is a multiple of 11, where x is a digit, what is the value of x?

Question 6:

If $\overline{98215x2}$ is a number with x as its tens digit such that is is divisible by 4. Find all possible values of x.

Question 7:

If x denotes the digit at hundreds place of the number $\overline{67x19}$ such that the number is divisible by 11. Find all possible values of x.

Question 8:

Find the remainder when 981547 is divided by 5. Do this without doing actual division.

Question 9:

Find the remainder when 51439786 is divided by 3. Do this without performing actual division.

Question 10:

Find the remainder, without performing actual division, when 798 is divided by 11.

Question 11:

Without performing actual division, find the remainder when 928174653 is divided by 11.

Question 12:

Given an example of a number which is divisible by
(i) 2 but not by 4.
(ii) 3 but not by 6.
(iii) 4 but not by 8.
(iv) both 4 and 8 but not by 32.

(i) 10
Every number with the structure (4n + 2) is an example of a number that is divisible by 2 but not by 4.

(ii) 15
Every number with the structure (6n + 3) is an example of a number that is divisible by 3 but not by 6.

(iii) 28
Every number with the structure (8n + 4) is an example of a number that is divisible by 4 but not by 8.

(iv) 8
Every number with the  structure (32n + 8), (32n + 16) or (32n + 24) is an example of a number that is divisible by 4 and 8 but not by 32.

Question 13:

Which of the following statements are true?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

(i) False
Every number with the structures (9n + 3) or (9n + 6) is divisible by 3 but not by 9. Example: 3, 6, 12 etc.
(ii) True
(iii) False
Every number with the structure (8n + 4) is divisible by 4 but not by 8. Example: 4, 12, 20 etc.
(iv) True
(v) False
Example: 24 is divisible by both 3 and 6 but it is not divisible by 18.
(vi) True
(vii) False
Example: 5 divides 10, which is a sum of 3 and 7. However, it neither divides 3 nor 7.
(viii) True
(ix) False
Example: 4 and 9 are co-prime numbers but both are composite numbers too.
(x) True

Question 1:

Solve each of the following Cryptarithms:

Question 2:

Solve each of the following Cryptarithm:

Question 3:

Solve each of the following Cryptarithm:

Question 4:

Solve each of the following Cryptarithm:

Question 5:

Solve each of the following Cryptarithm:

Question 6:

Solve each of the following Cryptarithm:

Question 7:

Show that the Cryptarithm $4×\overline{AB}=\overline{CAB}$ does not have any solution.

Question 1:

Without performing actual addition and division write the quotient when the sum of 69 and 96 is divided by
(i) 11
(ii) 15

(i) Clearly, 69 and 96 are two numbers such that one can be obtained be reversing the digits of the other. Therefore, when the sum of 69 and 96 is divided by 11, we get 15 (sum of the digits) as quotient.

(ii) Clearly, 69 and 96 are two numbers such that one can be obtained be reversing the digits of the other. Therefore, when the sum of 69 and 96 is divided by 15 (sum of the digits), we obtain 11 as quotient.

Question 2:

Without performing actual computations, find the quotient when 94 − 49 is divided by
(i) 9
(ii) 5

Question 3:

If sum of the number 985 and two other numbers obtained by arranging the digits of 985 in cyclic order is divided by 111, 22 and 37 respectively. Find the quotient in each case.