Question

Michael rode his bike 2 2/3 miles on saturday. He rode another 1 5/6 miles on Sunday. How many miles did Michael ride his bike on both days combined?

Answer 1

We are looking for a sum in this problem, the sum of the miles he rode on Saturday and Sunday.

First, let's change our values to improper fractions instead of mixed numbers:

$2 \dfrac{2}{3} = \dfrac{8}{3}$

$1 \dfrac{5}{6} = \dfrac{11}{6}$

Now, we have to find a common denominator so that we can add the fractions. This appears to be 6. Now, we can add the fractions by adding the numerator and keeping the common denominator the same:

$\dfrac{11}{6} + \dfrac{16}{6} = \dfrac{11 + 16}{6} = \dfrac{27}{6}$

Finally, we should convert this fraction back into a mixed number. You can see that we can take a 4 out of the improper fraction, leaving us with a $\frac{3}{6}$, or $\frac{1}{2}$. Our final answer is:

$\boxed{4\dfrac{1}{2}}$

Answer 2

To find the miles Michael rode, we can simply add up the miles he rode for both day:

$2 \frac{2}{3} + 1 \frac{5}{6} \\ = \frac{2 + 2 \times 3}{3} + \frac{5 + 6}{6} \\ = \frac{8 \times 2}{3 \times 2} + \frac{11}{6} \\ = \frac{16 + 11}{6} \\ = \frac{27}{6} \\ = 4 \frac{3}{6} \\ = 4 \frac{1}{2}$
Therefore the answer is 4 1/2 miles.

Hope it helps!