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### Grade 8 - Mathematics5.14 Theorem - II

 Theorem: Prove that the product of two odd number is an odd number. Proof: The general form of an odd number is 2n+1, where n is an integer. Let 2m+1 and 2n+1 are two different odd numbers, where m and n are integers. The product = (2m+1)(2n+1) = 2m(2n+1)+2n+1 = 4mn+2m+2n+1 = 2(2mn+m+n) + 1 (2m+1)(2n+1) = 2 (an integer) + 1 [Since, 2mn+m+n = an integer.] = an odd number. Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: 2*4*6*8*10 is ______ number.Even numberOdd number Q 2: 510 is _______ number.Odd numberEven number Q 3: 1000 - 562 is ______ number.Even numberOdd number Q 4: 49 is ______ number.Odd numberEven number Q 5: 546 + 352 + 42 + 31 is _____ number.Odd numberEven number Q 6: 1*2*3*4*5*6*7*8 is _____ number.Odd numberEven number Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!