To find the sum of \( \frac{1}{8} \) cup of cinnamon and \( \frac{1}{2} \) cup of sugar, we need to have a common denominator.
The denominators are 8 and 2. The least common denominator of these fractions is 8. We can convert \( \frac{1}{2} \) into an equivalent fraction with a denominator of 8:
\[ \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \]
Now we can add the two fractions:
\[ \frac{1}{8} + \frac{4}{8} = \frac{1 + 4}{8} = \frac{5}{8} \]
So, \( \frac{1}{8} + \frac{1}{2} = \frac{5}{8} \).
Interpretation in the Context of the Problem:
Micah is making a mixture of cinnamon and sugar for sprinkling on toast. The sum of \( \frac{1}{8} \) cup of cinnamon and \( \frac{1}{2} \) cup of sugar tells us that when combined, the total volume of the cinnamon and sugar mixture is \( \frac{5}{8} \) cup. This means that if Micah mixes these two ingredients together, he will have \( \frac{5}{8} \) cup of the mixture to sprinkle on his toast.