48. Since 48 contains 16, we disregard the 16. Multiplying 48 by 2, 3, etc., we see that 3×48, or 144, contains 9. Thus 144 is the least common denominator.

EXERCISES

For each of the columns below find the average. Arrange the work as shown in the preceding example.

6. In measuring a line segment six pupils of a class found the following results:

7. Draw five segments, each being longer than the preceding. Name them AB, CD, EF, GH, and IK. Measure each segment to the nearest sixteenth of an inch. Subtract their lengths in the following order: the first from the second, the second from the third, the third from the fourth, and the fourth from the fifth. State your results in the following form:

Exercises 8 to 28 give further practice in adding and subtracting fractions.

8. In the following subtract the lower number from the upper. Check each by adding the lower to the difference.

9. In each of the following subtract the lower from the upper number.

Find the following sums and differences. Arrange all work as shown in Exercise 10.

24. 18-10+

25. 1624-31

pounds. It is packed with

26. An empty soap box weighs 4 bars of soap weighing 543 pounds. By adding 41 and 541 find the weight of the box after packing.

27. The sum of two numbers is 301. One of the numbers is 163. Find the other by subtracting 163 from 301.

28. A table top 32 in. wide is to be made by glueing together 4 boards. How wide must be the fourth board if the widths of the others are respectively, 73 in., 7 in., and 8 in.?

29. In the drawing (Fig. 20) measure the length and the width of the frame of the picture, each to the nearest sixteenth of an inch. Add the length to the width.

30. In making a drawing of an object architects, designers, surveyors, and draftsmen usually do not draw a full-size picture. Each line in the drawing is made a specified part of the actual length.

FIG. 20

The object is then said to be drawn to scale. The following exercises show how actual length can be found in a scale drawing.

If an inch on the drawing (Fig. 20) represents a length of 8 inches in the frame of the picture, the actual length and width of the frame may be found by multiplying each of the measures in Exercise 29 by 8. Find the actual length and width of the frame.

31. The arrangement of the rooms on the first floor of a house (Fig. 21) is shown in the drawing (Fig. 22). One inch in the drawing represents 24 feet in the house. Find the approximate dimensions of the living room, dining room, kitchen, and porch.

32. Fig. 23 is a map of the State of Illinois. The segment AB in the lower left-hand corner represents a distance of 70 miles. It

is to be used to measure distances between places on the map to the nearest mile, just as we have used the ruler to measure the distance between the end points of a segment.

Fold a sheet of paper, and on the crease mark off the scale given on AB, making a graduated straightedge.

Using this as a ruler, find to the nearest mile the distance of each of the following cities from Chicago: Rockford, Quincy, Peoria, East St. Louis, Cairo, Danville.

FIG. 24

33. In the drawing (Fig. 24) an inch represents 2 ft., 6 in. Find the dimensions of the door.

Exercises 34 and 35 below give practice in such multiplications as occur in Exercise 33.

34. Multiply the following numbers, arranging your work as shown in the first exercise.