157. Written Problems. 1. How many yards are there in 25 pieces of carpeting if each piece contains 32.75 yards? 2. A mill uses 95.6 tons of coal per day. How many tons will it use in 42.25 days? 3. A cubic foot of water weighs 62.5 pounds; ice is .92 as heavy as water. What is the weight of a cubic foot of ice? 4. I bought 3 loads of wood, the first containing 1.04 cords, the second 1.05 cords, and the third .946 cord. What did it cost me at $4.50 a cord? 5. A gallon of water weighs 8.33 pounds. What is the weight of a gallon of milk which is 1.03 times as heavy as water? 6. A wheel in making one revolution travels 15.03 feet. How far will it travel in 25 revolutions? 7. A ship sails 18.54 miles in an hour. How far will she sail in 15.5 hours? 8. Find the cost of concreting a cellar 24.5 feet long by 14.25 feet wide, at 30 cents per square foot. 9. A quantity of provisions will last 25 men 12.75 days. How long will it last one man? 10. Two men start from the same place and travel in opposite directions, one at the rate of 3.85 miles per hour, and the other at the rate of 4.12 miles per hour. How far apart will they be at the end of 13 hours? Make a diagram. DIVISION OF DECIMALS. 158. Divide 42 by 2.1. Changing the decimal fraction in the divisor to a common fraction, we have 42 ÷ 2 = 42 ÷ 21 = 42 × 10 = 420. NOTE. - When we change the divisor 2.1 to 21, we have multiplied it by 10, and the same change must be made in the dividend. Make the divisor a whole number by removing the decimal point, and make a corresponding change in the dividend. The number of decimal places in the quotient will be equal to the number in the dividend as changed. Remove the decimal point in the divisor three places to the right, and make a corresponding change in the dividend, adding two ciphers. To show where the decimal point originally belonged, draw a canceliation mark through it, instead of erasing it. 15 100. 013.)196,300. 13 66 65 13 When the divisor is thus made a whole number, the decimal point in the quotient will be placed under (or over) the new decimal point in the dividend. 161. Divide, carrying out the quotient to 3 places of NOTE. To multiply .042 by 100, the decimal point is moved two places to the right; i.e. .042 × 100 4.2; .042 × 200 = 4.2 × 2 = 8.4. = NOTE. Remember that 369 ÷ 1000=36% = 369 thousandths=.369. To divide 369 by 3000, therefore, divide .369 by 3. Cancel the ciphers in the divisor, and remove the decimal point in the dividend a corresponding number of places to the left, prefixing ciphers if necessary. 1200)1.72,8 1200).01,728 .00144 Ans. 1. I cut 8.72 yards of cloth into 8 equal pieces. How long was each piece? 2. I divided .75 of a pound of candy equally among 3 girls. What part of a pound did each receive? 3. I divided .5 of a pound of cherries among 4 children. What part of a pound did each receive? 4. 49 rods is .7 of the distance round a field. How many rods of fence will enclose the field? 5. 24 yards of matting cover .8 of my floor. How many yards more must I buy? 6. 40 pounds are .4 of my weight. What do I weigh? 7. I spent 2.5 dollars, which was .5 of what I had. How much had I? 8. 36 square inches are .25 of a square foot. How many square inches in a square foot? 9. A collector receives .05 of all the money he collects. How much did he collect to earn $15? 10. At 75 cents each, how many chairs can be bought for $12? 166. Written Problems. 1. If 35.84 cubic feet of water weigh a ton, what will be the weight of 2458.6 cubic feet? 2. How many francs are there in $150? (A franc equals 19.34.) 3. If a barrel of flour costs $5.75, how many be bought for $258.75? barrels can 4. If $640.05 are paid for 75.3 tons of coal, what is the price per ton? 5. There are 31.5 gallons in a barrel. How many barrels are there in 2787.75 gallons? 6. I have 96 cubic feet of wood; this is .75 of a cord. How many cubic feet in 1 cord? 7. A man earns $162 in 13.5 weeks. What are his wages per week? 8. I bought a farm of 71.5 acres for $6220.50. What did it cost me per acre? 9. There are 2150.4 cubic inches in a bushel. How many bushels are there in 9676.8 cubic inches? 10. The wheel of a bicycle is 7.25 feet around. many times will it turn in going a mile, or 5280 feet? How |