Important Questions Class 8 Maths Chapter 16

Important Questions Class 8 Mathematics Chapter 16 – Playing With Numbers

Mathematics requires analytical thinking and problem-solving skills. One should do lots of practice and develop a deep understanding of the concepts of the subject in order to excel in Mathematics.

Chapter 16 of Class 8 Mathematics is about Playing with Numbers. The important topics covered in this chapter are:

• Introduction 
• Numbers in general form
• Games with numbers
• Letters for digits
• Tests of divisibility

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As we all have come across the phrase “Practice makes a man perfect” and hence to gain mastery in Mathematics, one needs to practise solving mathematical questions on a regular basis. Extramarks is a promising online learning platform that understands the significance of solving problems when it comes to Mathematics. 

Our experienced Mathematics faculty experts have prepared question-bank Class 8 Mathematics Chapter 16 Important Questions, after doing proper research and the past years’ question paper analysis. Important Questions Class 8 Mathematics Chapter 16 will provide the students with substantial questions relevant to the chapter Play with Numbers so that they can learn better and practise them for their examinations. Our teachers have given step-by-step instructions for each solution making it easy for students to comprehend and remember the concepts used in these solutions.

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Important Questions Class 8 Mathematics Chapter 16 – With Solutions

Given below are a few of the important questions and their solutions those are included in our Mathematics Class 8 Chapter 16 important questions:

Question 1: Write in the normal form 10 × 6 + 5.

• 65

• 56

• 25

• 54

Answer 1: (a) 65

Explanation 1: 10 × 6 + 5 = 60 + 5 = 65

Question 2: If the division of N ÷ 5 leaves a remainder of 1, what might be the one’s digit of N?

• 1

• Either 7 or 2

• 6

• 5

Answer 2: (c ) 6

Explanation 2: 5 + 1= 6 

Therefore, one’s digit of N is 6.

Question 3: The difference between a two-digit number and the number obtained by reversing its digits is always divisible by ____________

Answer 3: 9

Explanation 3: Taking a and b as the two digits, we get X = ab

On reversing the digits, we get Y = ba

Hence, the sum of digits in X is 10a + b and the sum of digits of Y is 10b + a

On subtracting X and Y, we get  

9a – 9b = 9 (ab)

Therefore, the number is divisible by 9

Question 4: A four-digit number abcd is divisible by 11, if d + b = ___________ or ___________.

Answer 4: a + c or b + d

Explanation 4: Implying the divisibility rule of 11, if abcd is divisible by 11, 

then a – b + c – d = 0

Therefore, we get a + b = b + d or each should be zero.

Question 5:     A       B

                   +  3       7

.                 —————-

                       6        A

                  —————-

Answer 5: Here, we see that B = 5 so that 7 + 5 = 12

Putting 2 at one’s place and carrying over 1 and A = 2, we get 

2 + 3 + 1 = 6

This A = 2 and B = 5

Question 6: Find the values of the letters in the following and give reasons for each step involved

•          2          A

                            +         6             A           B

                           —————————————

                                       A             0           9

                           —————————————

Answer 6: Taking A = 8 and B = 1, we find that 8 + 1 = 9 

On again adding 2 + 8 = 10

Thus, 10’s place will have a 0 and carry over 1.

Now, 1 + 6 + 1 = 8 = A

Therefore, A = 8 and B = 1

Question 7: Express the given number in a normal form:

(2×1000) + (2×10)

Answer 7: e can write (2×1000) + (2×10) in a normal form in the following way

(2×1000) + (2×10) = 2000 + 20 = 2020

Question 8:  What is the smallest number you have to add to 100000 to get a multiple of 1234?

Answer 8: 00000 can also be written as 1234 × 81 + 46

Thus, 1234 + 46 = 1188

Hence, the required number is 1188.

Question 9: Check the divisibility of 2146587 by 3.

Answer 9: The sum of the digits of  2146587 is 2 + 1 + 4 + 6 + 5 + 8 + 7 = 33

33 is divisible by 3 since 3 × 11 = 33

Hence, 2146587 is divisible by 3

Question 10: If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?

Answer 10: We are given that 31z5 is a multiple of 3. 

Following the divisibility rule of 3, 

We understand that the sum of the digits 31z5 need to be divisible by 3 for the number to be divisible by 3.

Which is, 3 + 1 + z + 5 = 9 + z

Therefore, 9 + z will be a multiple of 3

And it will be possible only when 9 + z is any of the values – 0, 3, 6, 9, 12, 15, 18 and further.

If z = 0, then 9 + z = 9 + 0 = 9

if z = 3, then 9 + z = 9 + 3 = 12

if z = 6, then 9 + z = 9 + 6 = 15

if z = 9, then 9 + z = 9 + 9 = 18

So we see that the value of 9 + z can be 9 or 12 or 15 or 18.

Hence we can conclude that 0, 3, 6 or 9 are four possible answers for z.

Question 11: If 24x is a multiple of 3, where x is a digit, what is the value of x?

Answer 11: Given that 24x is a multiple of 3.

Then we know that following the visibility rule off 3, the sum of all the digits of 24x should be a multiple of 3.

2 + 4 + x = 6 + x

Therefore, 6 + x is a multiple of 3, which is possible only when x is one the following numbers – 0, 3, 6, 9, 12, 15, 18 and so on.

X being a digit, the value of x shall either be 0 or 3 or 6 or 9, and the sum shall be either 6 or 9 or 12 or 15, respectively.

Hence, x shall be any of the four values – 0, 3, 6 or 9.

Question 12: A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.

Answer 12: Let the unit place digit be x and tens place digit be y.

Therefore, Equation (1) is 10y + x

 From the question, a two-digit number is 3 more than 4 times the sum of its digits

Now, the above condition suggests that the Equation (2) is 4(y + x) + 3

Equating equation 1 and 2

              4(y + x) + 3 = 10y + x

• 4x + 4y + 3 = 10y + x
• 3x – 6y = -3
• X – 2y = -1                  …equation (3)

Now, the second condition suggests that if 18 is added to the number, it’s digit is reversed

Therefore, Equation 4 is 10x + y

By the given condition, 

        ( 10y + x ) + 18 = 10x + y

• 10y + x = 10x + y -18
• 9y -9x = -18
• y – x = -2.                   …equation (5)

Solving equations 3 and 5, we get x = 5 and y = 3.

Benefits of Solving Important Questions Class 8 Mathematics Chapter 16

Mathematics requires a lot of practice for students of Classes 8, 9 and 10. Practice on a daily basis strengthens the roots of every concept. By practising Extramarks Important Questions Class 8 Mathematics Chapter 16, students will be able to have a strong grasp of the concept of the chapter and will also gain enthusiasm for solving all kinds of problems. 

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Following are some benefits of regularly solving questions from our Important Questions Class 8 Mathematics Chapter 16:

1. Our team of experienced Mathematics experts have curated a set of questions that covers all topics from Chapter 16. These questions from our Important Questions Class 8 Mathematics Chapter 16 are carefully chosen after analysing all the past years’ papers, NCERT textbooks and exemplars.
2. The questions and answers strictly abide by the CBSE syllabus and are in accordance with the CBSE guidelines, so that students can completely count on them.
3. Appropriate formulas have been used while answering Chapter 16 Class 8 Mathematics Important Questions for the students to understand and solve the questions in a better way.·   
4. Solutions are written in a cohesive and well-structured way. Students can study from it without having to look elsewhere for any assistance. This is true for all subjects.

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4. Important Formulas List
5. CBSE extra questions