Points to Remember - Playing with Numbers Class 8 Notes | EduRev

Class 8 Mathematics by Full Circle

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Class 8 : Points to Remember - Playing with Numbers Class 8 Notes | EduRev

The document Points to Remember - Playing with Numbers Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.
All you need of Class 8 at this link: Class 8

Points to Remember 
• A two digit number can Points to Remember - Playing with Numbers Class 8 Notes | EduRev be written in generalized form as 10 Points to Remember - Playing with Numbers Class 8 Notes | EduRev
• A three digit number can Points to Remember - Playing with Numbers Class 8 Notes | EduRev be written in generalized form as 100 Points to Remember - Playing with Numbers Class 8 Notes | EduRev
• Generalized form of numbers are helpful in solving puzzles or number games.
• A number is divisible by 10, if its ones digits is 0.
• A number is divisible by 5, if its ones digits is 0 or 5.
• A number is divisible by 2, if its ones digits is 0, 2, 4, 6 or 8.
• A number is divisible by 9, if the sum of its digits is divisible by 9.
• A number is divisible by 3, if the sum of its digits is divisible by 3.

We Know That
Numbers are of various types such as natural numbers, whole numbers integers, fractional and rational numbers. They are full of fun and magic. We also know about the various divisibility tests of numbers. We can enjoy, the magic and wonder of numbers For example,
9 x 1 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
9 x 2 = 18 → 1 + 8 =  Points to Remember - Playing with Numbers Class 8 Notes | EduRev
9 x 3 = 27 → 2 + 7 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
9 x 123 = 1107 → 1 + 1 + 0 + 7 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
1234 x 9 = 11106 → 1 + 1 + 1 + 0 + 6 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
12345 x 9 = 111105 → 1 + 1 + 1 + 1 + 0 + 5 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
123456 x 9 = 1111104 → 1 + 1 + 1 + 1 + 1 + 0 + 4 = Points to Remember - Playing with Numbers Class 8 Notes | EduRev

NUMBERS IN GENERAL FORM
We can express a number in general form using place value system, we may call it the expanded form of the number. LetPoints to Remember - Playing with Numbers Class 8 Notes | EduRev is a two digit number. We can write it in generalized form as Points to Remember - Playing with Numbers Class 8 Notes | EduRev Similarly, a 3-digit number Points to Remember - Playing with Numbers Class 8 Notes | EduRev can be written as
  Points to Remember - Playing with Numbers Class 8 Notes | EduRev

Games with numbers
Reversing the digits (2-digit number)
Example: Sudaram considered any number of 2-digits.
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Writing the given number in generalized form:
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Reversing the digits and writing the new number in generalized form:
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Adding, we get
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
i.e. he got
11 x [Sum of the digits of the chosen number]

Reversing The Digits and Subtracting
Let Sundaram chooses a number Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Generalised form = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Reversing the digits, new numberPoints to Remember - Playing with Numbers Class 8 Notes | EduRev
Generalised form = Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Subtracting
Points to Remember - Playing with Numbers Class 8 Notes | EduRev (when a > b)
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Points to Remember - Playing with Numbers Class 8 Notes | EduRev[Difference of the digits of the chosen number]
or
Points to Remember - Playing with Numbers Class 8 Notes | EduRev (when b > a)
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Points to Remember - Playing with Numbers Class 8 Notes | EduRev [Difference of the digits of the chosen number]

Reversing The Digits of A 3-Digit number

Note: 
When we reverse the digits of a 3-digit number then the middle digit (i.e. tens digit) remains unchanged.

Letters for Digit 

Note: 
For problems of addition and multiplication, we follow the following rules while during various puzzles.

(i) Each letter in a puzzle must stand for just one digit and each must be represented by just one
letter.
(ii) The first digit of a number cannot be zero.

Example: Find A and B such that
Points to Remember - Playing with Numbers Class 8 Notes | EduRev
Solution: We have to choose B such that B x 3 Points to Remember - Playing with Numbers Class 8 Notes | EduRev
It is possible for B = 0 or B = 5
Now, let us look for A,
If
A = 1, then AB x AB
10 x 13 = 130    For B = 0
or
15 x 13 = 195      For B = 5
which is less than 570 or 575
If A = 3, then
30 x 33 = 990  For B = 0
and
35 x 33 = 1155  For B = 5
which is greater than 570 or 575
If A = 2, then
20 x 23 = 460            For B = 0
and
25 x 23 = 575            For B = 5
The first possibility (20 x 23) fails but
The second one is correct
∴ The required values of A and B are
A = 2 and B = 5            
Points to Remember - Playing with Numbers Class 8 Notes | EduRev

Solve Examples:
Question 1. On multiplying 121  and its reverse, we get
a. 14641
b. 14541
c. 14441
d. None of the above.
Solution: 
A is the correct option. The reverse of 121 is 121, hence 121 × 121 = 14641.

Question 2. Which of the numbers are in general form?
a. 2 × 100 + 3 × 10 + 7
b. 2 × 10 + 3× 10 + 7
c. 2 × 100 + 2 × 100 + 7
d. 2 × 100 + 3 × 10 + 7
Solution: 
A is the correct option. The general form of any three digits is
abc = a× 100 + b × 10+ c
So, 237 = 2 × 100 + 3 × 10 + 7
So only one expression is in general form.

Question 3: The units digit of every prime number (other than 2 and 5 ) must be necessarily
a. 1, 3 0r 5
b. 1, 3, 7 or 9
c. 7 or 9
d. 1 or 7
Solution: 
B is the correct option.. All the even numbers are composite so prime numbers cannot end with any of the digits 0, 2, 4, 6, 8. Therefore units digit of every prime number (other than 2 and 5) must be necessarily 1, 3, 7 0r 9.

Question 4: Which of the following numbers is divisible by 14?
a. 4683
b. 7321
c. 1428
d. 5631
Solution: 
C is the correct option. The divisibility rule for 14 is that if the number is divisible by both 2 and 7 then the number is exactly divisible by 14. Here the last digit is, even so, the number 1428 is divisible by 2. 1428 is multiple of 7 so this number is also divisible by 7.

Question 5. Three common multiples of 18 and 16 are
a. 18, 6, 9
b. 18, 36, 6
c. 36, 54, 72
d. None
Solution: 
C is the correct option. The multiple of 18 is 18, 36 and 54. Multiples of 6 are 6, 12 and 18. Here the first common multiple will be 18. the next common multiple will be multiples of 18. The first three common multiples of 18 and 6 are 18, 36 and 54.

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