Class 6 Maths Chapter 3 Extra Questions Number Play
Class 6 Maths Number Play Extra Questions
NCERT Class 6 Maths Chapter 3 Number Play Extra Questions and Answers
Question 1.
Check if the Collatz Conjecture holds for the given numbers: 35, 22, 19, 18.
Answer:
As per Collatz Conjecture rule, starts with any number; if the number is even, take half of it; if the number is odd, multiply it by 3 and add 1; and repeat till to reach 1.
The sequence formed with starting number 35 is as follows:
35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1
The sequence formed with starting number 22 is as follows:
22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
The sequence formed with starting number 19 is as follows:
19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8,4, 2, 1.
The sequence formed with starting number 18 is as follows:
18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
Hence, the Collatz Conjecture holds for the given numbers: 35, 22, 19, 18.
Question 2.
Colour or mark the supercells in the table below.
Answer:
Question 3.
Estimate the following:
(a) 730 + 998
(b) 796 – 314
(c) 958 × 387
(d) 765 ÷ 95
Solution:
(a) 730 + 998
Since, 730 is closer to 700,
And, 998 is closer to 1000.
∴ Estimated sum = 700 + 1000
= 1700.
(b) 796 – 314
Since, 796 is closer to 800,
And, 314 is closer to 300.
∴ Estimated difference = 800 – 300
= 500.
(c) 958 × 387
Since, 958 is closer to 1000,
And, 387 is closer to 400.
∴ Estimated product = 1000 × 400 = 400000.
(d) 765 ÷ 95
Since, 765 is closer to 800,
And, 95 is closer to 100.
∴ Estimated quotient = 800 + 100 = 8.
Question 4.
Find the palindromic numbers by using the following 2-digit numbers:
59, 10, 15, 22 and 37 and also mention the required number of steps to make it a palindrome.
Solution:
For 59,
Step 1: Reverse of 59 is 95.
Add 59 + 95 = 154 (Not a palindrome).
Step 2: Reverse of 154 is 451.
Add 154 + 451 = 605 (Not a palindrome).
Step 3: Reverse of 605 is 506.
Add 605 + 506 = 1111 (which is a palindrome).
So, it takes 3 steps to reach a palindromic number 1111 starting from 59.
For 10,
Step 1: Reverse of 10 is 01.
Add 10 + 01 = 11 (which is a palindrome).
So, it takes 1 step to reach a palindromic number 11 starting from 10.
For 15,
Step 1: Reverse of 15 is 51.
Add 15 + 51 = 66 (which is a palindrome)
So, it takes 1 step to reach a palindromic number 66 starting from 15.
For 22,
As it is already a palindromic number. So, number of steps is 0.
For 37,
Step 1: Reverse of 37 is 73.
Add 37 + 73 = 110.
Step 2: Reverse of 110 is 011.
Add 110 + 011 = 121 (which is a palindrome).
So, it takes 2 steps to reach a palindromic number 121 starting from 37.
Thus, we reach the palindromes 1111, 11, 66, 22 and 121 for the numbers 59, 10, 15, 22 and 37 in steps 3, 1, 1, 0 and 2 respectively.
Question 5.
Case Based Question
Two friends Riya and Siya are playing a game, with 15 number play cards. The numbers written on them are as follows:
Riya has to pick a card from the first column, then Siya has to choose the cards from the 2nd or 3rd column, so that after adding or subtracting, they get the number equal to the 1st number.
Based on the above information, answer the following questions.
(a) If Riya chooses the number card with the number 25,900, then what are the number cards that can be choosen by Siya?
(b) Siya chooses the number cards 18,900, 900 and 60,000 for Riya’s number card 78,000, is Siya correct?
(c) Which number cards could be chosen by Siya for the number card 60,100?
Solution:
(a) As, Riya chose the number 25,900, the number cards chosen by Siya may be:
28,900; 7,900; 5,000 and 100
As, 28,900 – 7,900 + 5000 -100 = 21,000 + 4,900
= 25,900.
(Answer may vary)
(b) Yes, Siya is correct, as
60,000 + 18,900 – 900 = 78,900 – 900 = 78,000.
(c) Siya can choose the number cards: 60,000, 5000 and 4,900;
As, 60,000 + 5,000 – 4,900 = 60,100.
(Answer may vary)
