16_k=8
In the equation above, _ represents one of the operations of arithmetic: addition, subtraction, multiplication, or division. If k is a positive integer not equal to 8, what must be the value of k?
To find the value of k, we need to solve the equation 16 _ k = 8, where _ represents one of the operations of addition, subtraction, multiplication, or division. Let's examine each operation to see if any of them satisfy the given equation.
1. Addition: If we use addition, the equation becomes 16 + k = 8. To solve for k, we can subtract 16 from both sides: k = 8 - 16 = -8. However, the question states that k is a positive integer, so -8 is not a valid solution.
2. Subtraction: If we use subtraction, the equation becomes 16 - k = 8. Solving for k, we can subtract 8 from both sides: -k = 8 - 16 = -8. Multiplying both sides by -1 gives us k = 8.
3. Multiplication: If we use multiplication, the equation becomes 16 * k = 8. Dividing both sides by 16, we get k = 8 / 16 = 0.5. However, the question specifies that k must be a positive integer, so 0.5 is not a valid solution.
4. Division: If we use division, the equation becomes 16 / k = 8. Multiplying both sides by k gives us 16 = 8k. Dividing both sides by 8 gives us k = 16 / 8 = 2. This solution satisfies the condition that k is a positive integer and not equal to 8.
Therefore, the only valid value for k is k = 2.