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### Grade 8 - Mathematics5.1 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: When an integer is divided by 2, then the remainder is ____ or 1.0234 Q 2: The product of any two odd number is _______ number.Odd numberEven number Q 3: The sum of an even number and an odd number is ______ number.Even numberOdd number Q 4: The difference of an even number and an odd number is ____ number.Odd numberEven number Q 5: The product of any two even number is _______ number.Even numberOdd number Q 6: The sum of any two even numbers is ____ number.Even numberOdd number Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!