The trail is 3424 miles long . it begins in city a and ends in b. manfred has hiked 3/8 of that. how many miles has he hiked

All we need to do is to find out how much is 3/8 of 3424. We can do it in at least two ways:

1. Divide 3424 by 8 and then multiply the result by 3
2. Just multiply 3424 by 3/8

So:

3424 / 8 = 428
428 * 3 = 1284

or:

3424 * 3/8 =
= 428 * 3/1 =
= 428 * 3 =
= 1284

Manfred hiked 1284 miles.

Since he has hiked 3/8 of it.

=  3/8 * 3424
=  3 * 428 =      1284

= 1284 miles.