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

3 Answers
Feb 24, 2018

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!

Feb 24, 2018

She walked #15 21/40# miles in all.

Explanation:

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

#15 21/40#

Explanation:

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#