Page 107 - ArithBook5thEd ~ BCC

Mixed units are just like mixed numbers, because the smaller units are simple fractions of the larger
ones:
1 1 1
1in = ft 1 min = hr 1 sec = min.
12 60 60
It follows that measurements in mixed units can be added and subtracted just like mixed numbers. The
notion of proper form remains since, for example, a measurement of

4ft 17 in

makes sense, but is properly written as
5ft 5in,

since any measurement of over 12 inches is at least 1 foot. Borrowing and carrying are sometimes
needed, and are easily accomplished, as the next example shows.

Example 124. Hugo and Hector go to separate movies that start at the same time.Hugo’s movie is 2
hours and 5 minutes long, while Hector’s is 1 hour and 43 minutes.How long will Hector have to wait,
after his movie is over, for Hugo to come out?

Solution. Hector’s waiting time is the difference in the lengths of the movies,

2hr 5min
− 1hr 43min

The subtraction in the minutes column can’t be done, so we borrow 1 hr = 60 min from the hours
column, reducing the number of hours at the top of the hours column from 2 to 1, and increasing the
number of minutes at the top of the minutes column from 5 min to 5 min + 60 min = 65 min.

1hr 65min
− 1hr 43min
0hr 22min

Hector will have to wait 22 minutes.

Here’s an example involving length measurements.

Example 125. Two boards are laid end-to-end. One of the boards measures 6 ft 8 in,and the other
measures 11 ft 10 in. What is the total length of the boards? Give your answer in proper form.

Solution. We need to calculate the mixed-unit sum

6ft 8 in

+11 ft 10 in

Page 107