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

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

`8 1/8=(8*8+1)/8=65/8`

`7 2/5=(7*5+2)/5=37/5`

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

distance=`65/8+37/5`

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

distance=`325/40+296/40`

distance=`621/40`=`15 21/40` miles.

Hope this helps!

Jill walked `8 1/8` miles to a park i.e. `8+1/8` miles

and then `7 2/5` miles home i.e. `7+2/5` miles

In all she walked `8+1/8+7+2/5` miles

or `8+7+1/8+2/5` miles

or `15+(1xx5)/(8xx5)+(2xx8)/(5xx8)` miles

or `15+5/40+16/40` miles

or `15+(5+16)/40` miles

or `15+21/40` miles

i.e. `15 21/40` miles

We can do this a couple of ways.

Improper fractions

`8 1/8 + 7 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 `(8xx8+1)/8=65/8`

`65/8+37/5`

Now we need to have the denominators be the same:

`65/8(5/5)+37/5(8/8)=325/40+296/40`

`621/40`

And now we divide it back out:

`15.525=15 21/40`

~~~~~

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

`8 1/8 + 7 2/5=8+1/8+7+2/5=8+7+1/8+2/5=15+1/8+2/5`

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

`15+(1/8)(5/5)+(2/5)(8/8)`

`15+5/40+16/40=15+21/40=15 21/40`