19. A gallon of molasses is worth 25 cents, what is the value of 2 gallons ? Of 3 gallons ? Of 4 gallons ? Of 5 gallons ? Of 6 gallons ? 20. What cost 4 quarts of milk at 5 cents a quart ? and 8 gallons of vinegar at 10 cents a gallon ? 21. If a man earn 7 dolļars a week, how much will he earn in 3 weeks? In 4 weeks ? In 5 weeks? In 6 weeks ? In 7 weeks ? In 9 weeks ? 22. If one thousand feet of boards cost 12 dollars, what cost 4 thousand ? 5 thousand ? 6 thousand ? 7 thousand ? 12 thousand ? 23. In 1 pound there are 20 shillings, how many shillings in 3 pounds ? In 4 pounds ? In 6 pounds ? In 9 pounds ? 24. If 3 pair of shoes buy 1 pair of boots, how many pair of shoes will it take to buy 7 pair of boots ? 25. If 5 bushels of apples buy 1 arrel of flour, how many bushels of apples are equal in value to 12 barrels of flour ? The foregoing questions having been performed, it will be perceived, that Multiplication is a compendious way of performing Addition, and that it consists of three parts ; the multiplicand, or number to be multiplied ; the multiplier, or number to multiply by; and the result, which is called the product. The pupil, having thoroughly committed the multiplication Table, will notice the following RULE. Place the larger number uppermost, and then set the multiplier under it, so that units may be under units, f-c., and multiply by the multiplier, beginning at the unit's place and carry for tens as in addition. When the multiplier consists of more places than one, multiply each figure in the multiplicand by every figure in the multiplier, beginning with the units, and placing the first figure of each product directly under its multiplier, then add all their several products together in the same order, as they stand, and their sum will be the true product required. When there are ciphers between the significant figures of the multipliers, omit them, and multiply by the significant figures only. If there be ciphers at the right hand of the multiplier or multiplicand, they may be neglected in the operation, but their number must be affixed to the product. PROOF. Multiplication may be proved by division, or by multiplying the multiplier by the multiplicand, as in 12th and 13th questions, or by casting out the O's, thus ; cast the 9's from the multiplicand and place the remainder at the right hand of a cross, then cast the 9's from the multiplier and set the remainder at the left hand of the cross, then cast the 9's from the product, and set the remainder at the top of the cross. Multiply the numbers together on each side of the cross, and cast the 9's from their product, and if the remainder be like the number at the top of the cross, it may be presumed the work is right. See question 14. Answers. 17. Multiply 767853 by 9. 6910677. 18. Multiply 876538765 by 8. 7012310120. 19. Multiply 7654328 by 7. 53580296. 20. Multiply 4976387 by 5. 24881935. 21. Multiply 8765448 by 12. 105185376. 22. Multiply 4567839 by 11. 50246229. 23. Multiply 68759 by 5678. 390413602. 24. Multiply 78113 by 70005. 5468300565. 25. Multiply 46700 by 60103. 2806810100. 26. Multiply 83000 by 10007. 830581000. 27. Multiply 40009 by 40009. 1600720081. 28. What cost 14 barrels of apples at 3 dollars per barrel ? Ans. 42 dollars. 29. What cost 17 tons of hay at 18 dollars per ton ? Ans. 306 dollars. 30. What cost 47 cords of wood at 7 dollars per cord ? Ans. 329 dollars. 31. What cost 47 hogsheads of molasses at 13 dollars per hogshead ? Ans. 611 dollars. 32. What cost 97 oxen at 29 dollars each ? Ans. 2813 dollars. 33. Sold a farm containing 367 acres, what was the amount at 97 dollars per acre ? Ans. 35599 dollars. 34. An army of 17006 men receive each 109 dollars as their annual pay; what is the amount paid the whole army y? Ans. 1853654 dollars. 35. If a mechanic deposit annually in the Savings Bank, 407 dollars, what will be the sum deposited in 27 years ? Ans. 10989 dollars. 36. If a man travel 37 miles in one day, how far will he travel in 365 days? Ans. 13505 miles. 37. If there be 24 hours in one day, how many hours in 365 days? Ans. 8760 hours. 38. How many gallons are in 87 hogsheads, there being 63 gallons in each hogshead ? Ans. 5481 gallons. 39. If the expenses of the Massachusetts Legislature be 1839 dollars per day, what will be the amount in a session of 109 days? Ans. 200451 dollars. 40. If a hogshead of sugar contains 368 pounds, how many pounds in 187 hogsheads ? Ans. 68816 pounds. Section 5. DIVISION. MENTAL EXERCISES. 1. A gentleman divided 6 apples between 2 boys; how many did each receive ? 2. A farmer received 8 dollars for 2 sheep; what was the price of each ? 3. A man gave 15 dollars for 3 barrels of flour ; what was the cost of each barrel ? 4. A lady divided 20 oranges among her 5 daughters ; how many did each receive ? 5. If 4 casks of lime cost 12 dollars, what is the value of 1 barrel ? 6. A laborer earned 48 shillings in 6 days; what did he receive per day? 7. A man can perform a certain piece of labor in 30 days ; how long will it take 5 men to do the same ? 8. When 72 dollars are paid for 8 acres of land ; what cost 1 acre ? What cost 3 acres ? 9. If 21 pounds of flour can be obtained for 3 dollars, how much can be obtained for 1 dollar ? How much for 8 dollars ? How much for 9 dollars ? 10. Gave 56 cents for 8 pounds of raisins ; what cost 1 pound? What 7 pounds ? 11. If a man walk 24 miles in 6 hours, how far will be walk in 1 hour ? How far in 10 hours ? 12. Paid 56 dollars for 7 hundred weight of sugar ; what cost 1 hundred weight ? What cost 10 hundred weight ? 13. If 5 horses will eat a load of hay in one week, how long would it last one horse ? 14. In 20, how many times 2 ? How many times 4? How many times 5? How many times 10? 15. In 24 how many times 3 ? How many times 4? How many times 6 ? How many times 8 ? 16. How many times 7 in 21 ? In 28 ? In 56 ? In 35 ? In 14 ? In 63 ? In 77 ? In 70 ? In 84 ? 17. How many times 6 in 12 ? In 36 ? In 18 ?. In 54 ? In 60 ? In 42 ? In 48 ? In 72 ? In 66 ? The pupil will now perceive, that Division is a short or compendious way of performing Subtraction. Its object is to find how often one number is contained in another. It consists of four parts, the dividend, or number to be divided ; the divisor, the number we divide by ; the quotient, which shows how many times the divisor is contained in the dividend ; and the remainder, which is always less than the divisor, and of the same name of the dividend. I. When the divisor is less than 13, the question should be performed by SHORT DIVISION. 1. Divide 7554 dollars equally among 6 men. Dividend. In performing this question, inDivisor 6 ) 7554 quire how many times 6, the divi sor, is contained in 7, which is 1 Quotient 1 259 time, and I remaining ; write the |