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If h is even, j is odd, and k is odd, wh...

If h is even, j is odd, and k is odd, what is `k(h+j)`?

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To solve the problem step by step, we need to analyze the given information about the variables \( h \), \( j \), and \( k \): 1. **Identify the Types of Numbers**: - \( h \) is even. - \( j \) is odd. - \( k \) is odd. 2. **Understand the Properties of Even and Odd Numbers**: - An even number can be expressed as \( 2n \) for some integer \( n \). - An odd number can be expressed as \( 2m + 1 \) for some integer \( m \). - The sum of an even number and an odd number is odd. - The sum of two odd numbers is even. - The product of two odd numbers is odd. - The product of an even number with any number (even or odd) is even. 3. **Calculate \( h + j \)**: - Since \( h \) is even and \( j \) is odd, we can use the property that the sum of an even number and an odd number is odd. - Therefore, \( h + j \) is odd. 4. **Multiply \( k \) with \( (h + j) \)**: - Now, we need to calculate \( k(h + j) \). - Since \( k \) is odd and \( (h + j) \) is odd (as established in the previous step), we can use the property that the product of two odd numbers is odd. - Thus, \( k(h + j) \) is odd. 5. **Final Result**: - The final result of \( k(h + j) \) is odd. ### Summary of the Solution: - \( h + j \) is odd. - \( k(h + j) \) is odd. ### Final Answer: The result of \( k(h + j) \) is **odd**.
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