# Jill walked 8 1/8 miles to a park and then 7 2/5 miles home. How many miles did she walk in all?

Feb 24, 2018

Okay, I think the easiest way to approach this problem is to first convert the mixed fractions to irregular fractions:

$8 \frac{1}{8} = \frac{8 \cdot 8 + 1}{8} = \frac{65}{8}$

$7 \frac{2}{5} = \frac{7 \cdot 5 + 2}{5} = \frac{37}{5}$

We want the total number of miles, so our equation is:

distance=$\frac{65}{8} + \frac{37}{5}$

The LCD of 5 and 8 is 5*8=40, so:

distance=$\frac{325}{40} + \frac{296}{40}$

distance=$\frac{621}{40}$=$15 \frac{21}{40}$ miles.

Hope this helps!

Feb 24, 2018

She walked $15 \frac{21}{40}$ miles in all.

#### Explanation:

Jill walked $8 \frac{1}{8}$ miles to a park i.e. $8 + \frac{1}{8}$ miles

and then $7 \frac{2}{5}$ miles home i.e. $7 + \frac{2}{5}$ miles

In all she walked $8 + \frac{1}{8} + 7 + \frac{2}{5}$ miles

or $8 + 7 + \frac{1}{8} + \frac{2}{5}$ miles

or $15 + \frac{1 \times 5}{8 \times 5} + \frac{2 \times 8}{5 \times 8}$ miles

or $15 + \frac{5}{40} + \frac{16}{40}$ miles

or $15 + \frac{5 + 16}{40}$ miles

or $15 + \frac{21}{40}$ miles

i.e. $15 \frac{21}{40}$ miles

$15 \frac{21}{40}$

#### Explanation:

We can do this a couple of ways.

Improper fractions

$8 \frac{1}{8} + 7 \frac{2}{5}$

Make improper fractions by multiplying the whole number by the denominator, then add the numerator (so for instance with the first mixed number, we'll have $\frac{8 \times 8 + 1}{8} = \frac{65}{8}$

$\frac{65}{8} + \frac{37}{5}$

Now we need to have the denominators be the same:

$\frac{65}{8} \left(\frac{5}{5}\right) + \frac{37}{5} \left(\frac{8}{8}\right) = \frac{325}{40} + \frac{296}{40}$

$\frac{621}{40}$

And now we divide it back out:

$15.525 = 15 \frac{21}{40}$

~~~~~

We can avoid the large numbers by adding the whole numbers first, then adding the fractions:

$8 \frac{1}{8} + 7 \frac{2}{5} = 8 + \frac{1}{8} + 7 + \frac{2}{5} = 8 + 7 + \frac{1}{8} + \frac{2}{5} = 15 + \frac{1}{8} + \frac{2}{5}$

And now we add the fractions by finding a common denominator:

$15 + \left(\frac{1}{8}\right) \left(\frac{5}{5}\right) + \left(\frac{2}{5}\right) \left(\frac{8}{8}\right)$

$15 + \frac{5}{40} + \frac{16}{40} = 15 + \frac{21}{40} = 15 \frac{21}{40}$