Given:
distance between the shop and the first delivery is 12 1/3 miles.
The distance between the next three deliveries is 8 3/4 miles; 17 2/8 miles; and 23 2/3 miles respectively.
The distance from the final delivery to the shop is 10 5/10 miles
We simply add up all the distances and divide the sum by 5. However, we need to convert each mixed fractions into it improper fraction.
12 1/3 → 37/3
8 3/4 → 35/4
17 2/8 → simplify: 17 1/4 → 69/4
23 2/3 → 71/3
10 5/10 → simplify: 10 1/2 → 21/2
37/3 + 35/4 + 69/4 + 71/3 + 21/2
Find the LCD or least common denominator. It is the number that can factor all denominators.
LCD is 12.
(37/3 * 4/4) + (35/4 * 3/3) + (69/4 * 3/3) + (71/3 * 4/4) + (21/2 * 6/6)
148/12 + 105/12 + 207/12 + 284/12 + 126/12 = 870 / 12
Average distance:
870 / 12 ÷ 5 = 870 / 12 * 1/5 = 870 / 60 = 14.5 miles
The average distance for all segments of the trip is 14.5 miles.