The average of five consecutive even numbers is 14. What is the smallest of these numbers?

Sure, let's solve this step by step.

1. Understand the problem: We are given that the average of five consecutive even numbers is 14. We need to find the smallest of these numbers.

2. Define the consecutive even numbers: Let the five consecutive even numbers be: $x, x+2, x+4, x+6, x+8$ where $x$ is the smallest even number.

3. Calculate the average: The average of these five numbers is given by: $\text{Average} = \frac{x + (x+2) + (x+4) + (x+6) + (x+8)}{5}$

4. Simplify the sum: Combine the terms in the numerator: $x + (x+2) + (x+4) + (x+6) + (x+8) = 5x + 20$

5. Set up the equation: We know the average is 14, so: $\frac{5x + 20}{5} = 14$

6. Solve for $x$: Multiply both sides by 5 to clear the fraction: $5x + 20 = 70$ Subtract 20 from both sides: $5x = 50$ Divide by 5: $x = 10$

7. Conclusion: The smallest of these five consecutive even numbers is $x$, which is 10.

So, the smallest of the five consecutive even numbers is 10.