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NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

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Question 1: Write the following numbers in generalized form.

(i) 25        (ii) 73      
(iii) 129        (iv) 302

Solution:   

(i) 25 = 20 + 5

= 10 x 2 + 5 x 1 = 10 x 2 + 5

(ii)  73 = 70 + 3

 = 10 x 7 + 3 x 1 = 10 x 7 + 3

(iii) 129 = 100 + 20 + 9

= 100 x 1 + 10 x 2 + 1 x 9 = 100 x 1 + 10 x 2 + 9

(iv) 302 = 300 + 2

= 100 x 3 + 10 x 0 + 1 x 2 = 300 + 0 + 2
Question 2: Write the following in the usual form.
(i) 10 x 5 + 6     (ii) 100 x 7 + 10 x 1 + 8  
(iii) 100 x a + 10 x c + b
Solution: 
(i) 10 x 5 + 6 = 50 + 6 = 56
(ii) 100 x 7 + 10 x 1 + 8 = 700 + 10 + 8 = 718
(iii) 100 x a + 10 x c + b = 100a + 10c + b = NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Question 3: Check what the result would have been if sundaram had chosen the numbers shown below.

1) 27
Ans: Chosen number = 27
Nmber with reversed digits = 72
Sum of the two numbers = 27 + 72 = 99
Now, 99 = 11[9] = 11[2 + 7]
= 11[Sum of the digits of the chosen number]

2) 39
Ans: Chosen number = 39
Number with reversed digits = 93
Sum of the two numbers = 39 + 93 = 132
Now, 132 ÷ 11 = 12
i.e. 132 = 11[12] = 11[3 + 9]
= 11[Sum of the digits of the chosen number]
3) 64
Ans: Chosen number = 64
Number with reversed digits = 46
 Sum = 64 + 46 = 110
Now, 110 = 11[10] = 11[6 + 4]
= 11[Sum of the digits of the chosen number]
4) 17
Ans: Chosen number = 17
Number with reversed digits = 71
Sum = 17 + 71 = 88
Now,  88 = 11[8] = 11[1+ 7]
= 11[Sum of the digits of the chosen number]
Question 4: Check what result would have been if Sundaram had chosen the numbers shown.
1) 17
Ans: Chosen number = 17
Number with reversed digits = 71
Difference = 71 – 17 = 54
= 9 x [6]
 9 x [Difference of the digits of the chosen number (7 – 1 = 6)]
2) 21
Ans: Chosen number = 21
Number with reversed digits = 12
Difference = 21 – 12 = 9
= 9 x [1]
= 9 x [Difference between the digits of the chosen number (2 – 1 = 1)]
3) 96

Ans: Chosen number = 96
Number with reversed digits = 69
Difference = 96 – 69 = 27
= 9 x [3]
= 9 x [Difference between the digits of the chosen number (9 – 6 = 3)]
4) 37

Ans: Chosen number = 37
Number with reversed digits = 73
Difference = 73 – 37 = 36
= 9 x [4]
= 9 x [Difference between the digits of the chosen number (7 – 3 = 4)]
Question 5: Check what the result would have been if Minakshi had chosen the numbers shown below.

In each case keep a record of the quotient obtained at the end.
1) 132
Ans: Chosen number = 132
Reversed number = 231
Difference = 231 – 132 = 99
    We have, 99 ÷ 99 = 1, remainder = 0 
2) 469
Ans: Chosen number = 469
Reversed number = 964
Difference = 964 – 469 = 495
We have, 495 ÷ 99 = 5, remainder = 0
3) 737
Ans: Chosen number = 737
Reversed number = 737
We have Difference = 737 – 737 = 0
We have, 0 ÷ 99 = 0, remainder = 0
4) 901
Ans: Chosen number = 901
Reversed number = 109
Difference = 901 – 109 = 792
    We have, 792 ÷ 99 = 8, remainder = 0

Forming three-digit number with given three digits

Note: Generalised form of NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Generalised form ofNCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Generalised form of NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Adding NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

                                                     NCERT Solutions for Class 8 Maths - Playing with Numbers - 1 which is divisible by 37
Question 6: Check what the result would have been if Sudaram had chosen the numbers shown below.
1) 417
Ans: Chosen number = 417
Two other numbers with the same digits are 741 and 174
Sum of the three numbers:-
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1
We have 1332 ÷ 37 = 36, remainder = 0
2) 632
Ans: Chosen number = 632
Two other numbers are 263 and 326
Sum of the three numbers:-
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1
We have 1221 ÷ 37 = 33, remainder = 0
3) 117
Ans: Chosen number = 117
Other numbers are 711 and 171
Sum of the three numbers:-
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1
We have 999 ÷ 37 = 27, remainder = 0

4) 937
Ans: Chosen number = 937
Other two numbers are 793 and 379
Sum of the three numbers:-
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1
We have 2109 ÷ 37 = 57, remainder = 0

Exercise 16.1

Find the values of the letters in each of the following and give reasons for the steps involved.
Question 1:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

 Question 2:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Question 3:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Question 4:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Question 5:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
3 × B = B
⇒ B = D
3 × A = CA
⇒ 3 × 5 = 15
Thus A = 5 and C = 1
Hence A = 5, B = 0 and C = 1

Question 6:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
5 × B = B
⇒ B = 0 or 5
5 × A = CA
5 × 5 = 25
Only possible when B = 0
Thus A = 5 and C = 2
Hence A = 5, B = 0 and C = 2

Question 7:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
B × 6 = B
6 × 4 = 24 → B = 4 and 2 is carried to
6 × A = BB
⇒ 6 × 7 = 42 + 2 (carried on) = 44
Thus B = 7
Hence A = 7 and B = 4

Question 8:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
1 + B = 0
1 + 9 = 10 → unit digit is 0 and 1 is carried to A
+ 1 +1 (carried on) = B = 9
A + 2 = 9 ⇒ A = 9 – 2 = 7
Hence A = 7 and B = 9

Question 9:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
B + 1 = 8 ⇒ B = 8 – 1 = 7
A + B = a number with unit digit 1
A + B = 11
⇒ A + 7 = 11
⇒ A = 11 – 7 = 4 (1 Carried to)
Now 1 carried on + 2 + A = B
3 + A = 7
⇒ A = 7 – 3 = 4
Hence A = 4, B = 7

Question 10:
NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

Solution:
9 = A + B
9 = 1 + 8 or 2 + 7 or 3 + 6 or 4 + 5 or 8 + 1 or 7 + 2 or 6 + 3 or 5 + 4 or 0 + 9 or 9 + 0
Now 0 is required at unit place
2 + A = 10
⇒ A = 10 – 2 = 8
B = 9 – 8 = 1
1 + 6 + 1 (carried on) = A = 8
Hence A = 8 and B = 1

The document NCERT Solutions for Class 8 Maths - Playing with Numbers - 1 is a part of the Class 8 Course NCERT Textbooks & Solutions for Class 8.
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FAQs on NCERT Solutions for Class 8 Maths - Playing with Numbers - 1

1. How can I solve problems related to playing with numbers?
Ans. You can solve problems related to playing with numbers by understanding the concepts of factors, multiples, prime numbers, and divisibility rules. Practice solving different types of numerical problems to improve your skills.
2. What are some common mistakes to avoid while solving playing with numbers problems?
Ans. Some common mistakes to avoid while solving playing with numbers problems include mixing up factors and multiples, not applying divisibility rules correctly, and not considering all possible combinations when finding factors or multiples.
3. Can you explain the concept of prime numbers in playing with numbers?
Ans. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. Understanding prime numbers is essential for solving playing with numbers problems.
4. How can I improve my problem-solving skills in playing with numbers?
Ans. To improve your problem-solving skills in playing with numbers, practice solving a variety of numerical problems regularly. Familiarize yourself with different concepts such as factors, multiples, prime numbers, and divisibility rules to become more proficient in solving such problems.
5. Are there any online resources available to help me with playing with numbers problems?
Ans. Yes, there are several online resources such as educational websites, math forums, and video tutorials that can help you understand and solve playing with numbers problems. You can also find practice worksheets and quizzes to test your knowledge and skills in this area.
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