19. From 8054010657811 take 76909748598. Ans. 7977100909213. 20. From 7100071641115 take 10071178. Ans. 7100061569937. 21. From 501505010678 take 794090589. Ans. 500710920089. 22. Take 99999999 from 100000000. Ans. 1. 23. Take 44444444 from 500000000. Ans. 455555556. 24. Take 1234567890 from 9987654321. Ans. 8753086431. 25. From 800700567 take 1010101. Ans. 799690466. 26. Take twenty-five thousand twenty-five from twenty-five millions. Ans. 24974975. 27. Take nine thousand ninety-nine from ninety-nine thousand. Ans. 89901. 28. From one hundred one millions ten thousand one hundred one take ten millions one hundred one thousand and ten. Ans. 90909091. 29. From one million take nine. Ans. 9999991. 30. From three thousand take thirty-three. Ans. 2967. 31. From one hundred millions take five thousand. Ans. 99995000. 32. From 1,728 dollars, I paid 961 dollars; how many remain ? Ans. 767 dollars. 33. Our national independence was declared in 1776; how many years from that period to the close of the last war with Great Britain, in 1815 ? 31. The last transit of Venus was in 1769, and the next will be in 1874; how many years will intervene ? Ans. 105 years. 35. The State of New Jersey contains 6851 square miles, and Delaware 2120. How many more square miles has the former State than the latter ? Ans. 4731. 36. In 1810 the number of inhabitants in the United States was 17,069,453, and in 1850 it was 23,191,876; what was the increase ? Ans. 6,122,423. 37. In 1850 there were raised in the State of Ohio 56,619,608 bushels of corn, and in 1853, 73,436,690 bushels ; what was the increase ? Ans. 16,817,082 bushels. 38. By the census of 1850, 13,121,198 bushels of wheat were raised in New York, and 15,367,691 bushels in Pennsylvania; how many bushels in the latter State more than in the former ? Ans. 2,246,193 bushels. Ans. 39 years. 39. The city of New York owes 13,960,856 dollars, and Boston owes 7,779,855 dollars; how much more does New York owe than Boston ? Ans. 6,181,001 dollars. 40. From five hundred eighty-one thousand take three thou sand and ninety-six. Ans. 577,904. 41. It was ascertained by a transit of Venus, June 3, 1769 that the mean distance of the earth from the sun was ninety-five millions one hundred seventy-three thousand one hundred twentyseven miles, and that the mean distance of Mars from the sun was one hundred forty-five millions fourteen thousand one hundred forty-eight miles. Required the difference of their distances from the sun. Ans. 49,841,021 miles. Art. 33. Method of subtracting when there are two or more subtrahends. Ex. 1. A man owing 767 dollars, paid at one time 190 dollars, another time 131 dollars, at another time 155 dollars; how much did he then owe? Ans. 291 dollars. FIRST OPERATION. SECOND OPERATION. In the first opDollars. Dollars. eration, the several Minuend 7 67 Minuend 7 67 subtrahends, hav ing been properly 131 131 placed, are added 190 Subtrahends 190 for a single subtra155 155 hend, to be taken from the minuend. Subtrahend 476 Remainder 291 In the second, the Remainder 291 subtrahends subtracted, as they are added, at one operation, thus : beginning with units, 5 and 1 equal 6, which from 7 units leaves 1 unit; passing to tens, 5 and 9 and 3 equal 17 tens; reserving the left-hand figure to add in with the figures of the subtrahends in the next column, the right-hand figure, 7, being larger than 6 tens of the minuend, we add 10 to the 6, and, subtracting, have left 9 tens; and, passing to hundreds, we add in the left-hand figure 1 reserved from the 17 tens, and also add 1, equal 10 tens, to compensate for the 10 added to the minuend, and with the other figures, 1 and 1 and 1 equal 5 hundreds, which, taken from 7 hundreds, leave 2 hundreds; and 291 as the answer sought. 2. E. Webster owned 6,765 acres of land, and he gave to his oldest brother 2,196 acres, and his uncle Rollins 1,981 acres ; how much has he left ? Ans. 2,588 acres. 3. The real estate of James Dow is valued at 3,769 dollars, and his personal estate. at 2,648 dollars; he owes John Smith 1,728 dollars, and Job Tyler 1,161 dollars; how much is Dow worth? Ans. 3,528 dollars. are Ø IV. MULTIPLICATION. MENTAL EXERCISES. ART. 34. WHEN any number is to be added to itself several times, the operation may be shortened by a process called Multication. Ex. 1. If a man can earn 8 dollars th 1 week, what will he earn in 4 weeks? ILLUSTRATION. - It is evident, since a man can earn 8 dollars in 1 week, in 4 weeks he will earn 4 times as much, and the result may be obtained by addition; thus, 8+8+8+8= 32; or, by a more convenient process, by setting down the 8 but once, and multiplying it by 4, the number of times it is to be repeated; thus, 4 times 8 are 32. Hence in 4 weeks he will earn 32 dollars. MULTIPLICATION TABLE. QUESTION. — Art. 34. How may the process of adding a number to itself several times be shortened ? 2. What cost 5 barrels of flour at 6 dollars per barrel ? ILLUSTRATION. — If a barrel of four cost 6 dollars, 5 barrels will cost 5 times as much ; 5 times 6 are 30. Hence 5 barrels of flour at 6 dollars per barrel will cost 30 dollars. 3. What cost 6 bushels of beans at 2 dollars per bushel ? 4. What cost 5 quarts of cherries at 7 cents per quart ? 5. What will 7 quarts of vinegar cost at 12 cents per quart ? 6. What cost 9 acres of land at 10 dollars per acre ? 7. If a pint of currants cost 4 cents, what cost 9 pints? 8. If in 1 penny there are 4 farthings, how many in 9 pence? In 7 pence? In & pence? In 4 pence? In 3 pence? 9. If 12 pence make a shilling, how many pence in 3 shillings? In 5 shillings? In 7 shillings? In 9 shillings ? 10. If one pound of raisins cost 6 cents, what cost 4 pounds ? 5 pounds ? 6 pounds? 7 pounds? 8 pounds? 9 pounds ? 10 pounds ? 12 pounds ? 11. In one acre there are four roods; how many roods in 2 acres? In 3 acres ? In 4 acres? In 5 acres? In 6 acres ? In 9 acres ? 12. A good pair of boots is worth 5 dollars; what must I give for 5 pairs ? For 6 pairs ? For 7 pairs ? For 8 pairs ? For 9 pairs ? 13. A cord of good walnut wood may be obtained for 8 dollars; what must I give for 4 cords ? For 6 cords ? For 9 cords? 14. What cost 4 quarts of milk at 5 cents a quart, and 8 gallons of vinegar at 10 cents a gallon? 15. If a man earn 7 dollars 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 ? 16. If 1 thousand feet of boards cost 12 dollars, what cost 4 thousand ? 5 thousand ? 6 thousand ? 7 thousand ? 9 thousand ? 12 thousand ? 17. If 3 pairs of shoes buy 1 pair of boots, how many pairs of shoes will it take to buy 7 pairs of boots ? 18. If 5 bushels of apples buy 1 barrel of flour, how many bushels of apples are equal in value to 12 barrels of four ? 19. If 1 yard of canvas cost 25 cents, what will 12 yards cost? ILLUSTRATION. - The number 25 is composed of 2 tens and 5 units; 12 times 2 tens are 24 tens; and 12 times 5 units are 60 units, or 6 tens ; 24 tens added to 6 tens make 30 tens, or 300. Therefore, 12 yards will cost 300 cents, or 3 dollars. 20. In 1 pound there are 20 shillings; how many shillings in 3 pounds ? In 4 pounds? In 6 pounds ? 21. 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 ? Of 9 gallons ? 22. If 1 man earn 12 dollars in 16 days, how much would 10 men earn in the same time ? 23. If a steam-engine runs 28 miles in 1 hour, how far will it run in 4 hours? In 6 hours ? In 9 hours ? 24. If the earth turns on its axis 15 degrees in 1 hour, how far will it turn in 7 hours ? In 11 hours ? In 12 hours ? 25. In a certain regiment there are 8 companies, in each company 6 platoons, and in each platoon 12 soldiers; how many soldiers are there in the regiment ? 26. If 1 man walk 7 miles in 1 hour, how far will he walk in 8 hours ? In 9 hours? In 11 hours ? In 12 hours ? In 20 hours ? In 30 hours ? ART. 35. The learner, having performed the foregoing questions, will perceive that MULTIPLICATION is the process of taking a number as many times as there are units in another number. In multiplication three terms are employed, called the Multiplicand, the Multiplier, and the Product. The multiplicand is the number to be multiplied or taken. The multiplier is the number by which we multiply, and denotes the number of times the multiplicand is to be taken. The product is the result, or number produced by the multiplication. The multiplicand and multiplier are often called FACTORS. SIGNs. — The sign of multiplication is formed by two short lines crossing each other obliquely; thus, X. It shows that the numbers between which it is placed are to be multiplied together; thus, the expression 7 X 5 = 35 is read, 7 multiplied by 5 is equal to 35. QUESTIONS. Art. 35. What is multiplication? What three terms are employed ? What is the multiplicand ? What is the multiplier ? What is the product ? What are the multiplicand and multiplier often called ? What is the sign of multiplication ? What does it show? |