InterviewSolution
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InterviewSolution
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(i) Observe and complete:1 + 3 = ?5 + 11 = ?21 + 47 = ?___ + ____ = ?From this observation, we conclude that “the sum of any two odd numbers is always an _____”(ii) Observe and complete:5 × 3 = ?7 × 9 = ?11 × 13 = ?_____ × ____ = ?From this observation, we conclude that “the product of any two odd numbers is always an _____”Justify the following statements with appropriate examples:(iii) The sum of an odd number and an even number is always an odd number.(iv) The product of an odd and an even number is always an even number.(v) The product of only three odd numbers is always an odd number. |
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Answer» (i) 1 + 3 = 4 An odd number + another odd number = An Even number From this observation, we conclude that the sum of any two odd numbers is always an even number. (ii) 5 × 3 = 15 An odd number × Another odd number = An odd number From this observation, we conclude that “the product of any two odd numbers is always an odd number.” (iii) Take the odd number 5 and the even number 10 Their sum = 5 + 10 = 15, which is odd. ∴ Sum of an odd number and an even number is always an odd number. (iv) Take the odd number 5 and the even number 10. Their product = 5 × 10 = 50, which is even Thus the product of an odd and an even number is always an even number. (v) Consider 7 × 5 × 3 We know that the product of any two odd numbers is an odd number 7 × 5 = 35, odd number. Also we have 35 × 3 = 105 ∴ 7 × 5 × 3 = 105, an odd number. So the product of three odd numbers is always an odd number. |
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