### Instruction: You begin with $\frac{1}{2}$ scoop of ice cream.  Since you're hungry, you ask the vendor for $\frac{2}{7}$ more scoops of ice cream.  Then, you eat $\frac{5}{8}$ scoops.  How many scoops of ice cream are left on your cone?### Response: I need to find out how many scoops of ice cream I have in total, and then subtract how many scoops I ate.
To find the total, I need to add $\frac{1}{2}$ and $\frac{2}{7}$.
I can't add fractions with different denominators, so I need to find a common denominator.
The least common multiple of 2 and 7 is 14, so I can multiply both the numerator and denominator of $\frac{1}{2}$ by 7, and both the numerator and denominator of $\frac{2}{7}$ by 2, to get equivalent fractions with the same denominator.
That gives me $\frac{7}{14}$ and $\frac{4}{14}$.
Now I can add them by adding the numerators and keeping the denominator.
That gives me $\frac{11}{14}$.
So I have $\frac{11}{14}$ scoops of ice cream in total.
Now I need to subtract how many scoops I ate, which is $\frac{5}{8}$.
Again, I need a common denominator, and the least common multiple of 14 and 8 is 56.
So I can multiply both the numerator and denominator of $\frac{11}{14}$ by 4, and both the numerator and denominator of $\frac{5}{8}$ by 7, to get equivalent fractions with the same denominator.
That gives me $\frac{44}{56}$ and $\frac{35}{56}$.
Now I can subtract them by subtracting the numerators and keeping the denominator.
That gives me $\frac{9}{56}$.
So I have $\frac{9}{56}$ scoops of ice cream left on my cone.