Question

final round! this time, there is just one clue. write your answer as a mixed number.
clue: start at $9\frac{1}{3}$ and subtract $\frac{2}{3}$.
$9\frac{1}{3} - \frac{2}{3} = \boxed{?} \frac{\boxed{?}}{\boxed{?}}$

Explanation:

Step1: Subtract the fractions

The fractional parts are $\frac{1}{3}$ and $\frac{2}{3}$. Since $\frac{1}{3}<\frac{2}{3}$, we need to borrow 1 from the whole number part. So $9\frac{1}{3}$ becomes $8 + 1+\frac{1}{3}=8+\frac{3}{3}+\frac{1}{3}=8\frac{4}{3}$.

Step2: Subtract the mixed numbers

Now subtract the fractional parts: $\frac{4}{3}-\frac{2}{3}=\frac{2}{3}$. Then subtract the whole number parts: $8 - 0 = 8$ (since the second number has no whole number part other than what's in the mixed number, and we already adjusted the first number). So $8\frac{4}{3}-\frac{2}{3}=8\frac{2}{3}$? Wait, no, wait. Wait, original number is $9\frac{1}{3}$, borrow 1 (which is $\frac{3}{3}$) to make the fraction part $\frac{1 + 3}{3}=\frac{4}{3}$. Then subtract $\frac{2}{3}$ from $\frac{4}{3}$: $\frac{4}{3}-\frac{2}{3}=\frac{2}{3}$. Then the whole number part: $9 - 1 = 8$ (because we borrowed 1). So $8+\frac{2}{3}=8\frac{2}{3}$? Wait, no, wait, let's do it again. $9\frac{1}{3}$ is equal to $\frac{9\times3 + 1}{3}=\frac{28}{3}$. $\frac{2}{3}$ is just $\frac{2}{3}$. Subtract them: $\frac{28}{3}-\frac{2}{3}=\frac{26}{3}$. Convert $\frac{26}{3}$ to mixed number: $8\frac{2}{3}$ (since $8\times3 = 24$, $26 - 24 = 2$). Wait, but maybe a simpler way: $9\frac{1}{3}-\frac{2}{3}$. Since the denominators are the same, subtract the numerators of the fractions: $1 - 2$ is negative, so we take 1 from the whole number 9, making it 8, and add $\frac{3}{3}$ to the fraction: $8 + \frac{3 + 1}{3}=8\frac{4}{3}$. Then subtract $\frac{2}{3}$: $8\frac{4 - 2}{3}=8\frac{2}{3}$. Wait, but maybe I made a mistake. Wait, $9\frac{1}{3}-\frac{2}{3}$. Let's think of it as $(9 + \frac{1}{3})- \frac{2}{3}=9+(\frac{1}{3}-\frac{2}{3})=9 - \frac{1}{3}=8\frac{2}{3}$. Yes, that's correct. Because $\frac{1}{3}-\frac{2}{3}=-\frac{1}{3}$, so $9-\frac{1}{3}=8\frac{2}{3}$.

Answer:

$8\frac{2}{3}$