Question

myra did a running drill to get in shape for soccer season. first, myra ran 2/3 of a mile. then she ran 1/3 of a mile and 1/3 of a mile. after a break, myra ran 2/3 of a mile and finally 1/3 of a mile more. how many miles did myra run in total?
miles
submit

Explanation:

Step1: List all distances

Myra's runs: $\frac{2}{3}$, $\frac{1}{3}$, $\frac{1}{3}$, $\frac{2}{3}$, $\frac{1}{3}$ miles.

Step2: Sum the fractions

Add them: $\frac{2}{3} + \frac{1}{3} + \frac{1}{3} + \frac{2}{3} + \frac{1}{3}$. Combine numerators: $\frac{2 + 1 + 1 + 2 + 1}{3} = \frac{7}{3}$? Wait, no: 2+1+1+2+1=7? Wait, 2+1=3, +1=4, +2=6, +1=7? Wait, no, wait: $\frac{2}{3} + \frac{1}{3} = 1$, then +$\frac{1}{3}$ = $1\frac{1}{3}$, +$\frac{2}{3}$ = $2$, +$\frac{1}{3}$ = $2\frac{1}{3}$? Wait, no, let's recalculate:

Wait, $\frac{2}{3} + \frac{1}{3} + \frac{1}{3} + \frac{2}{3} + \frac{1}{3}$ = ($\frac{2}{3} + \frac{2}{3}$) + ($\frac{1}{3} + \frac{1}{3} + \frac{1}{3}$) = $\frac{4}{3} + \frac{3}{3}$ = $\frac{4}{3} + 1$ = $\frac{7}{3}$? No, $\frac{3}{3}$ is 1, so $\frac{4}{3} + 1$ = $\frac{7}{3}$ ≈ 2.333? Wait, no, wait: 2/3 +1/3 is 1, then +1/3 is 1 1/3, +2/3 is 2, +1/3 is 2 1/3, which is 7/3? Wait, 2 1/3 is 7/3? Yes, because 2 is 6/3, plus 1/3 is 7/3. Wait, but let's check again:

Wait, the distances are: first $\frac{2}{3}$, then two $\frac{1}{3}$s, then $\frac{2}{3}$, then $\frac{1}{3}$. So total: $\frac{2}{3} + \frac{1}{3} + \frac{1}{3} + \frac{2}{3} + \frac{1}{3}$. Let's count the number of 2/3 and 1/3: two 2/3s (total $\frac{4}{3}$) and three 1/3s (total $\frac{3}{3} = 1$). So $\frac{4}{3} + 1 = \frac{4}{3} + \frac{3}{3} = \frac{7}{3}$? Wait, no, 4/3 + 3/3 is 7/3, which is 2 and 1/3. Wait, but maybe I made a mistake. Wait, 2/3 +1/3 is 1, +1/3 is 1 1/3, +2/3 is 2, +1/3 is 2 1/3. Yes, 2 1/3 is 7/3. Wait, but let's add again:

$\frac{2}{3} + \frac{1}{3} = 1$

$1 + \frac{1}{3} = 1\frac{1}{3}$

$1\frac{1}{3} + \frac{2}{3} = 2$

$2 + \frac{1}{3} = 2\frac{1}{3}$

Which is $\frac{7}{3}$ miles. Wait, but is that correct? Wait, 2/3 +1/3 +1/3 +2/3 +1/3: numerators 2+1+1+2+1=7, denominator 3, so 7/3, which is 2 1/3. Yes.

Answer:

$\frac{7}{3}$ (or $2\frac{1}{3}$)