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Grade 8 - Mathematics
5.1 Theorem - I

Theorem:
The sum or difference of any two even numbers is an even number.

Proof:
An even number is a number which leaves remainder '0' when divided by 2.
The general form of an even number is 2n, where n is an integer.
Let 2m and 2n are any two numbers, m and n are integers.
Their sum = 2m+2n
= 2(m+n)
= 2 * an integer [ Since, m+n = an integer ]
= 2 * l
If 'l' is odd or even but 2l is always even.
Difference of two even numbers.
2m-2n = 2(m-n)
= 2 * an integer.
= 2 * p
If 'p' is odd or even but 2p is always even.


Directions: Choose the correct answer. Also write at least ten examples of your own.
Q 1: 2,4,6,8,.... are divided by 2 then the remainder is _______.
2
1
4
0

Q 2: When an integer is divided by 2, then the remainder is ____ or 1.
3
4
2
0

Q 3: The sum of any two even numbers is ____ number.
Odd number
Even number

Q 4: The sum of any two odd numbers is _____ number.
Odd number
Even number

Q 5: The difference of an even number and an odd number is ____ number.
Even number
Odd number

Q 6: The sum of an even number and an odd number is ______ number.
Even number
Odd number

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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