CHAPTER V

PROBLEMS OF MEASUREMENT

You have learned to measure certain things that you have had to use, or in order to answer questions in which you were interested. To measure a line, you took some measure a foot long or a yard long and applied it to the line you wished to measure and found how many times it was contained. To measure a box or basket of nuts, you measured them out in a quart measure and found how many quarts it contained. The measure you used was called the unit of measure.

To measure anything is to find how many standard units of measure it will contain.

MEASURING LENGTHS: THE TABLE OF LINEAR MEASURE

1. Count the 1-inch measures on a 1-foot rule.

2. Count the 1-foot measures on a 1-yard rule.

3. On the blackboard or floor measure off a line 16 ft. 6 in. long (16 ft. long.) This length is called a rod.

4. With a line 1 rd. long, measure off 40 rd. or mi.

5. If you live on a long straight road or street, measure off 80 rd. or 1 mi. and try to get a notion of how long a mile is.

6. Name some placemi. from school. Try to think of a place twice as far away and thus be able to think how much mi. is.

7. Make a line on the blackboard that you think is 8 in. long. Measure it to see how accurately you estimated. 8. Estimate the width of your schoolroom. Measure it to see how accurate you were.

9. Estimate the height of the door. Measure it to see how accurate you were.

10. Estimate and measure the length of the city block upon which your school stands, school stands, using separately, feet, yards, and rods.

EXPRESSING FRACTIONAL MEASURES

1. The 1-inch measures divide a 1-foot rule into how many equal parts? Then 1 in. is what part of a foot? 2. Express as a fractional part of 1 ft. :

3 in.; 5 in.; 6 in.; 8 in.; 10 in.; 11 in.

3. Instead of saying that a line is 4 ft. 6 in. long, we may express it in feet alone by saying what?

4. Express as feet :

2 ft. 8 in.; 3 ft. 3 in.; 5 ft. 9 in.; 6 ft. 2 in.; 8 ft. 10 in.

5. Instead of saying that John is 4 ft. 8 in. tall, we may say that he is how many feet tall? Instead of using feet, we may say that he is how many inches tall?

EXPRESSING FRACTIONAL MEASURES

125

6. Express the feet and inches in problem 4 in inches. Thus, 2 ft. 8 in. = 2 x 12 in. + 8 in. = 32 in.

7. James is building a dog kennel. using calls for a board 5 ft. long. 51 inches must he measure off?

Think, "ft. = 1 of 12 in.

The plan that he is

How many feet and

= 3 in. So 51 ft.

= 5 ft. 3 in."

8. Express as feet and inches:

31 ft.; 6 ft.; 73 ft.; 55 ft.; 81 ft.; 61 ft.

9. Into how many equal parts do the 1-inch spaces divide a yardstick? Then 1 inch is what part of 1 yard?

10. Express as a fraction of a yard and reduce to lowest terms: 12 in.; 18 in.; 24 in.; 9 in.; 27 in.; 6 in.

11. Into how many equal parts do the 1-foot measures divide a yardstick? Then 1 ft. is what part of 1 yd.? 2 ft. are what part of a yard?

Ribbons, laces, trimmings, and cloth are sold by the yard. You should ask for yards and fractions of a yard, not for feet and inches.

12. Mary wants a piece of ribbon 1 yd. 12 in. long. How much must she ask for?

13. Helen needs 2 yd. 9 in. of trimming. For how much must she ask the clerk?

14. Express in yards: 3 yd. 12 in.; 5 yd. 18 in.; 1 yd. 24 in.; 2 yd. 27 in.

15. Express as yards and inches: 12 yd.; 23 yd.; 57 yd. 16. Express as feet and fractions of a foot: 30 in.; 50 in.; 98 in.; 75 in.; 86 in.; 125 in.

17. Express as yards and fractions of a yard: 8 ft.; 10 ft.; 16 ft.; 25 ft.; 38 ft.; 50 ft.; 40 in.; 60 in.; 80 in.

BUYING FRACTIONAL LENGTHS

1. Frank needed a steel rod 4 ft. 8 in. long to make a trapeze. What will it cost him at 18¢ per foot?

2. Henry and his brother were building a slide. A carpenter sold them a smooth, wide board 14 ft. 9 in. long and charged them 24¢ a foot for it. Find the cost.

3. In building a yard for his hens, Ralph needed 6 pieces of lumber each 4 ft. 8 in. long. He found that the price was 8¢ per foot. Find the cost.

4. In making a sail for an ice boat, Donald needs 2 pieces of canvas each 62 in. long. At 68¢ per yard, how much will it cost him?

5. Lucile wanted 8 pieces of wide ribbon each 24 in. long to make some bags for a fair. How much will it cost her at 54¢ per yard?

6. Helen's mother wants enough toweling to make 5 towels each 1 yd. 9 in. long. At 36¢ per yard, how much will it cost her?

7. To trim a dress, Dorothy needs one piece of lace 27 in. long, and two pieces each 12 in. long. At 48¢ per yard, how much will it cost?

8. Grace's mother wants enough aprons, allowing 1 yd. 27 in. to each. material cost her at 38¢ per yard?

material to make 3 How much will the

9. Name some things you buy by the foot, give the price you would have to pay, and find the cost of the lengths you might need.

10. Name some things sold by the yard and give the price. Give lengths you would need for certain purposes and find the cost.

ADDING YARDS, FEET, AND INCHES 127

ADDING YARDS, FEET, AND INCHES

1. In repairing his rabbit hutch, Ralph needed three pieces of board: one, 2 ft. 8 in. long; one, 3 ft. 9 in. long; and the third 4 ft. 6 in. long. To get it all in one board, how long must it be?

He could have found it in either of two ways.

2. Tell which way you prefer and why you prefer it. Add in both ways:

3. 5 ft. 4 in.; 6 ft. 9 in.; 3 ft. 10 in.; 3 ft. 3 in.

4. 3 ft. 6 in.; 2 ft. 8 in.;

5. 5 ft. 4 in.; 2 ft. 6 in.;

5 ft. 7 in.; 3 ft. 5 in.

4 ft. 11 in.; 5 ft. 5 in.

6. 4 ft. 2 in.; 5 ft. 1 in.; 3 ft. 10 in.; 4 ft. 7 in.

7. Helen needs three pieces of ribbon: one piece, 1 yd. 12 in.; one, 2 yd. 8 in.; and one, 1 yd. 18 in. If bought in one piece, how much should she buy?

8. Ralph has a board 10 ft. long. He needs two pieces each 2 ft. 8 in. long, and one piece 5 ft. 4 in. long. Can he get all three pieces from this board?

9. Add:

3 yd. 13 in. + 4 yd. 24 in. + 6 yd. 16 in. + 1 yd. 2 in.