Question

eliza bikes $1\frac{3}{10}$ miles to the store. then she bikes $\frac{4}{10}$ mile to the library.
what is the total distance eliza bikes? write your answer as a mixed number.
$1\frac{7}{10}$ miles
after she leaves the library, eliza bikes $\frac{2}{10}$ mile to the post office.
now, what is the total distance eliza bikes? write your answer as a mixed number.
$?\frac{?}{?}$ miles

Explanation:

First Part (Store to Library)

Step1: Convert mixed number to improper fraction

The distance to the store is \(1\frac{3}{10}\) miles. To convert this mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{3}{10}=\frac{1\times10 + 3}{10}=\frac{13}{10}\) miles.

Step2: Add the two distances

The distance to the library is \(\frac{4}{10}\) miles. Now we add the distance to the store and the distance to the library: \(\frac{13}{10}+\frac{4}{10}=\frac{13 + 4}{10}=\frac{17}{10}\) miles.

Step3: Convert back to mixed number

To convert \(\frac{17}{10}\) back to a mixed number, we divide 17 by 10. \(17\div10 = 1\) with a remainder of 7. So, \(\frac{17}{10}=1\frac{7}{10}\) miles.

Second Part (Store to Library to Post Office)

Step1: Use the previous total distance

From the first part, the total distance to the library was \(1\frac{7}{10}\) miles (or \(\frac{17}{10}\) miles as an improper fraction).

Step2: Add the distance to the post office

The distance to the post office is \(\frac{2}{10}\) miles. Now we add this to the previous total: \(\frac{17}{10}+\frac{2}{10}=\frac{17+2}{10}=\frac{19}{10}\) miles.

Step3: Convert back to mixed number

Dividing 19 by 10 gives \(19\div10 = 1\) with a remainder of 9. So, \(\frac{19}{10}=1\frac{9}{10}\) miles.

Answer:

First total distance: \(1\frac{7}{10}\) miles.
Second total distance: \(1\frac{9}{10}\) miles.