Subtracting Compound Numbers Sight Exercises 1. Give remainders: b. 2 pk. 1qt. c. 1 bu. 1 pk. d. 3 gal. 2 qt. a. 1 pk. - 5 qt. 1. From a barrel of oil containing 45 gal., 28 gal. 2 qt. are sold. How many gallons remain? 1. An automobile uses 19 gal. 2 qt. of gasoline in 6 da. How many gallons and quarts does it use, on an average, per day? 2. Divide: a. 23 lb. 2 oz. ÷ 5 d. 33 bu. 1 pk. +7 b. 16 pk. 4 qt. +6 c. 69 lb.÷8 e. 31 gal. 2 qt.÷9 f. 80 yd.÷3 3. When a machine uses gasoline at the rate of 3 gal. 2 qt. per day, how long will 84 gal. last? Measurements - Areas of Rectangles Preparatory Exercises 1. (a) How many inches are there in each side of a 1-foot square? (b) How many square inches are there in a square 12 inches long and 12 inches wide? (c) How many square inches are there in a square foot? 2. (a) How many feet are there in each side of a 1-yard square? (b) How many square feet are there in a square 3 feet long, 3 feet wide? (c) How many square feet are there in a square yard? 3. (a) How many square yards are there in a square 5 yards long, 5 yards wide? (b) How many square yards are there in a square rod? 1. A field is 40 rods long, 40 rods wide. (a) How many square rods does it contain? (6) How many acres? 2. What are the dimensions of a square field containing 1600 square rods? 3. (a) What fraction of a square mile is there in a field mile square? (b) How many acres? 4. It takes a mile of wire fencing to enclose a square field. (a) What fraction of a square mile does the field contain? (b) How many acres? Written Problems 1. How many acres are there in a field 60 rods wide, 2. How many acres are there in a city block (a) 16 rods wide and 40 rods long? mile wide and mile long? (b) 3. (a) How many feet wide is a block, including its share of the street, when there are 20 blocks to a mile? How long is a block when (6) there are 8 blocks to a mile? (c) 6 blocks to a mile? (d) 10 blocks to a mile? 4. At $2 per square yard, find the cost of a concrete sidewalk 9 ft. wide, 20 ft. long. Preparatory Exercises 1. The top layer of a box of caramels has 4 rows of 3 caramels each. (a) How many caramels are there in the top layer? (6) In the bottom layer? (c) How many caramels does the box contain if there are two layers? 2. How many 1-inch cubes could be placed in a box 6 inches long, 5 inches wide, 4 inches deep, inside measurement? 3. What is the capacity of a box 4 ft. long, 3 ft. wide, 2 ft. deep? Volumes of Rectangular Solids The term solid, in connection with measurements, is applied as well to an empty box as to a brick; and the term volume is used to denote the capacity of the former and also the cubic contents of the latter. A rectangular solid has six faces, each of which is a rectangle. Sight Problems 1. How many cubic inches are there in a brick (a) 8 inches long, 4 inches wide, 2 inches thick? (b) 8 inches long, 4 inches wide, 2 inches thick? 2. What fraction of a cubic foot is there in a brick ft. long, ft. wide, & ft. thick? ᄒ 3. (a) How many cubic feet are there in a 3-foot cube? (b) How many cubic yards? (c) How many cubic feet are there in a cubic yard? Written Exercises 1. How many cubic inches are there in a 12-inch cube ? 2. At 231 cubic inches to the gallon, how many cubic inches are there in 7 gallons? 3. At 1 cubic feet to the bushel, (a) what fraction of a bushel is 1 cubic foot? (b) What decimal? 4. How many cubic inches are there in 14 cubic feet? 5. A cubic foot of water weighs 62 pounds. Find the weight of a gallon of water, taking 71 gallons to the cubic foot. 6. How many ounces does a cubic foot of water weigh? Surfaces of Rectangular Solids Sight Problems 1. How many square yards are there (a) in the floor of a room 6 yards long, 5 yards wide? (b) In the ceiling of a room 18 feet long, 15 feet wide? If the room is 9 feet high, (c) how many square yards are there in each of the two larger walls? (d) In each of the two smaller walls? 2. The top of a brick measures 8 inches by 4 inches. (a) What fraction of a square foot would the bottom of a brick cover? (b) How many would be required to cover a square foot? One side of a brick measures 4 inches by 2 inches. (c) What fraction of a square foot would the side of a brick cover? (d) How many bricks laid on the side would cover a square foot? 3. How many square feet of sheet iron are there in the sides and the bottom of a tank 6 feet long, 5 feet wide, and 4 feet deep, allowing 1 square foot for overlapping at the joints? Sight Exercises 1. Give in square inches the areas of rectangles having dimensions as follows: |