Any REMAINDER, which appears after the operation of division, is the numerator of a fraction, the divisor beiny the denominator; and this fraction forms a part of the quotient. Therefore, place the remainder and the divisor, as a fraction, to the right of the quotient. - . 2. At $2 per yard, how many yards of cloth can be bought for $49; that is, how many whole yards, and what part of another yard can be bought ? 3. How many times 2 are there in 49 ? 4. How much flour can be bought for $639, at $5 per barrel; that is, how many barrels, and what part of another barrel can be bought ? 5. In 639, how many times 5; that is, how many fives, and what part of another 5, in 639 ? 6. How much salt can be bought for 87 shillings, at 4 shillings per bushel ? 7. Suppose a rail-way car to run 16 miles an hour in how many hours will it run 350 miles ? 8. How many times 12 are there in 1049 ? Observe that 1s. is zo of £1; therefore the remainder in this example, may be expressed as a fraction. 11. How many yards of cloth can be bought for 549 shillings, at £1 per yard ? 12. Suppose a ton of hay to be equal in value to 34 bushels of oats; how many tons of hay must be given for 450 bushels of oats ? 13. How many times 17 are there in 23 times 31 ? 14. How much rice, at $4 per cwt., must be given for 620 lb. of cheese, at 10 cents per pound ? SECTION 14. CHANGE OF WHOLE NUMBERS TO FRACTIONS. | How many thirds are there in 14 ? 14 In 1 there tre 3-thirds; 3 therefore, there are 3 times as many thirds as whole ones, 42-thirds. Ans. 42. in any whole number. RULE. To change a whole number to an inproper fraction, multiply the whole number by the denominator, and the product will be the numerator. 2. If you cut 17 sheets of paper into half-sheets, how many halves will there be ? 3. How many fifths of a dollar are there $ 16 ? 7. If a stage run 1 mile in of an hour, how many miles would it run in 126 hours? 8. How many fourths are there in 152? 153 In this example, we add the 3-fourths to the fourths produc ed by the multiplication of 15 63-fourths. by 4, and thus obtain Note. A whole number and a fraction expressed together, thus, 154, is called a mixed number. 9. How many eighths of a mile in 57 miles ? 12. If } of a dollar will pay for 1 gallon of beer, how much beer can be bought for $64 ? 13. If of a dollar will pay for 3 yards of ribbon, how many yards can be bought for $63? Section 15. CHANGE OF FRACTIONS TO WHOLE NUMBERS.. 1. How many whole ones are there in 42 ? 3)4 2-thirds. Since make a whole 1, there are as many whole ones in 42 14 wholes as there are times 3 in 42. RULE. To change an improper fraction to a whole number, divide the numerator by the denominator, anci the quotient will be the whole number. 2. How many whole sheets of paper must be cut into ualves, to make 49 of a sheet? 3. In 24,5 of a dollar, how many dollars ? 6. If a stage run 1 mile in of an hour, how many hours would it be in running 126 miles ? 7. Change 32.2 to a whole number. 8. Suppose 8 pounds of sugar can be bought for $1; now many pounds will 2650 of a dollar pay for ? 9. Change 97 to a mixed number? 5)87 We divide the 87-fifths by 5, and obtain 17 whole ones: then, there are 17 ; 2-fifths over, making 17. 10. Change 249 to a mixed number. 11. How many dollars are there in 507 of a dollar 2 12. How many gallons in of a gallon ? 13. If } of a dollar will pay for 1 pound of coffee, hou many dollars will 312 pounds of coffee cost? 14. If 1 pound of butter cost Ž of a dollar, what would be the price of 491 pounds, at the same rate ? Section 16. 1. Add together i, ii, 14, ii, 11 and . The sum of these fractions will be an improper fraction, and it must be changed to a mixed number. : 2. What is the sum of 491 11, 7511 and 836 41 ? 4914 In this example, we add together 7511 the elevenths, and find their sum to 836 6 be {}; which is equal to 21. The 11 we write down, and carry the 2 to 140411 the column of units. 3. What is the sum of 4194, 185, 124, 85734, 91, 251%, 141, and 254 ? 4. Add together 33l 35, 141, 9701 , 28, 15815, 1240-25, 9, 1004, and in 5. Subtract 1376 from 2258. 22583 We cannot take from , therefore, 18765 we join 1 unit with the , making , and take from . We then proceeu 3817 to take 6 units from 7 units. 6. Subtract 460314 from 71706. 8. If 175 yards of cloth be cut from a piece contain ing 49 yards, how much will be left ? 9. A retailer put into a firkin, 28 pounds of butter at one time, 19 1 pounds at another, and 35 17 pounds at another, and then sold out 25 15 pounds. How many pounds still remained in the firkin? SECTION 17. 1. Suppose a rail-road car to run of a mile 'n ! minute; what distance will it run in 47 minutes ? 2. How many whole ones in 47 times ? 3. If of a yard of broad-cloth will make 1 jacke, how many yards will it take to make 18 jackets? 4. How many whole ones in 18 times ? 5. If of a pound of gunpowder tea cost 1 dollar, how many pounds can be bought for 50 dollars ? 6. How many whole ones in 50 times ? Section 18. 1. What is the product of 86%, multiplied by 9 ? 864 We multiply by 9 thus, 9 times ö? is 36 ; equal to 54. Then we write this | under the #, and carry the 5 to 7797 the product of the 6 units. 2. What is the product of 41%, multiplied by 7 ? 3. What is the value of a field, which contains 5 acres, allowing it to be worth 54 dollars per acre ? . 4. How much is 4 times 35 13? 5 How much is 9 times 14731 24 ? E How much is 28 times 54s? 54 Here we are obliged to multiply by 28 8 units and 2 tens separately, and we 432 cannot well bring in the product of the fraction by the 2 tens. Therefore, 18? we first multiply the whole numbers, and then find 28 times in a separate 1530 operation, which is not here written. 108 7. How much is 92 times 20516? 9. How niany gallons of wine are there in 31 casks, 10. A merchant paid $75 42 apiece, for 47 mules. 11. If a steam-boat run 236 15 miles in 1 day, what 12. How much is 15 times 27 ? 14. If a horse eat 12 of a bushel of oats a day, how Section 19. 1. If į of a chest of tea be worth $6.87}, what is 2. If io of a dollar will pay for travelling 27 miles on a turnpike road, how far can you go for $ 1 ? 4. If of a kite line be 25 yards in length, what is the whole length of the line ? 6. If a man can earn 12 cents in of a day, what sum of money can he earn in 1 day? 7. If of a yard of gold wire be worth 15 of a dollar, what is the value of 1 yard of the wire ? Section 20. 1. A boy having $ 2, gave of his money for a knife. What fraction of 1 dollar did the knife cost? 2. of 2 is equal to what part of 1? 3. 6 men divided 5 barrels of flour equally among them, each man taking of the flour in each barrel. What fraction of a barrel did each man get ? 4. } of 5 is equal to what part of 1 ?. 5. If you should take it of a bushel of corn from each of 10 bushels, what fraction of 1 bushel would you obtain ? 6. What part of 1 is to of 10? |