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According to parity rules, what is the result of Even × Odd?
- a)Even
- b)Odd
- c)Prime
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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According to parity rules, what is the result of Even × Odd?a)Evenb)Od...
Multiplying any number with an even number always gives an even product.
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According to parity rules, what is the result of Even × Odd?a)Evenb)Od...
Understanding Parity Rules
In mathematics, particularly in number theory, the concept of parity refers to whether an integer is even or odd.
Definitions:
- Even Number: An integer that is divisible by 2 (e.g., -4, -2, 0, 2, 4).
- Odd Number: An integer that is not divisible by 2 (e.g., -3, -1, 1, 3).
Multiplication of Even and Odd Numbers:
When we multiply an even number by an odd number, the result is always even.
Explanation:
- An even number can be represented as 2n, where n is an integer.
- An odd number can be represented as 2m + 1, where m is also an integer.
Now, when you multiply them:
- Even × Odd = (2n) × (2m + 1)
- Distributing gives: 2n * 2m + 2n * 1 = 4nm + 2n
The result, 4nm + 2n, is clearly divisible by 2, confirming that the product is even.
Conclusion:
Hence, the result of multiplying an even number by an odd number is always an even number. Therefore, the correct answer to the question "What is the result of Even × Odd?" is:
Answer: Even (Option A)
In mathematics, particularly in number theory, the concept of parity refers to whether an integer is even or odd.
Definitions:
- Even Number: An integer that is divisible by 2 (e.g., -4, -2, 0, 2, 4).
- Odd Number: An integer that is not divisible by 2 (e.g., -3, -1, 1, 3).
Multiplication of Even and Odd Numbers:
When we multiply an even number by an odd number, the result is always even.
Explanation:
- An even number can be represented as 2n, where n is an integer.
- An odd number can be represented as 2m + 1, where m is also an integer.
Now, when you multiply them:
- Even × Odd = (2n) × (2m + 1)
- Distributing gives: 2n * 2m + 2n * 1 = 4nm + 2n
The result, 4nm + 2n, is clearly divisible by 2, confirming that the product is even.
Conclusion:
Hence, the result of multiplying an even number by an odd number is always an even number. Therefore, the correct answer to the question "What is the result of Even × Odd?" is:
Answer: Even (Option A)
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