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26. A cow that cost $152 was sold at an advance of $19.25. What was she sold for?

27. A man bought a village lot for $1265. He paid $25 for taxes, and sold it for $1106. How much did

he lose?

28. A horse, harness, and saddle were bought for $375. Paid for repairs on the harness $1, and on the saddle $2. Sold the horse and harness for $293, the saddle for $18. Was there gain or loss, and how much?

29. A man owing $7862.50 has paid $5678. How much. is still due?

30. From a $50 bank-note a bill of $38.50 was paid. What change was given back?

31. A man left his property to his wife and two children.

To his wife $3794; to his daughter $1478 less than to his wife; to his son $325 less than to his daughter. What did the daughter and son receive, and what was the whole sum divided?

32. The length of the Missouri river from its source to the Mississippi is three thousand ninety-six miles, and from its source to the Gulf of Mexico four thousand five hundred six miles. How many miles is it from the junction of the two rivers to the Gulf of Mexico?

33. The sum of 4 numbers is eight hundred ninety-seven.

thousand six. The first is eighty-five thousand three hundred seven, the second is twenty-five thousand nine hundred eighty-seven more than the first, the third is twelve thousand four hundred sixty-two less than the second. What is the fourth?

34. A gentleman received from his father $65,784. He paid for a house, $18,620; for furniture, $6,978;

for a carriage and a pair of horses, $3000. What had he left?

35. A's estate is thirty-six thousand five hundred eight minus nine thousand eight hundred seventy-two dollars. B's estate is forty-three thousand five hundred twenty-four dollars more than A's. What is the value of B's estate?

36. A merchant invested ninety-six thousand dollars in a ship: the first year he made three thousand seven hundred ninety-five dollars; the second year he made four hundred fifty dollars; the third year he lost four thousand two hundred forty-five. Did he gain or lose by the investment, and how much? 37. In 1860 St. Louis had a population of one hundred sixty-thousand seven hundred seventy-three; Cincinnati, one hundred sixty-one thousand forty-four. In 1870 St. Louis had three hundred ten thousand eight hundred sixty-four inhabitants; Cincinnati, two hundred sixteen thousand two hundred thirtynine. What was the increase of each? What was the excess of the increase of one above that of the other?

38. Mr. Smith paid fifteen thousand nine hundred eightyseven dollars for his farm, implements, and stock. The stock cost three thousand six hundred dollars, the implements one thousand four hundred eightysix dollars. Required the value of the farm.

39. How many hours from eight o'clock in the morning until five o'clock in the afternoon?

40. Four men, A, B, C, D, bought a factory for $78,960. A was to pay $12,607; B, $3,000 more than A; C, $8,000 more than B. What had D to pay?

CHAPTER IV.

MULTIPLICATION.

49. If the cost of 6 tons of coal at $7 a ton is required, the amount can be found by writing $7 six times in a column convenient for adding, as in the margin, and finding the sum of the column.

50. If the cost of a whole cargo of coal was required, this operation would be long and tedious, and therefore a shorter process has been devised, called Multiplication.

$7

7

7

7

$42

By this process $7 is written only once, 6 is written beneath the $7 to show the number of times $7 must be taken in order to obtain the required amount, and this amount is found by saying 6 times $7 are $42. Thus:

$7
6

$42

51. In this operation $7 is called the multiplicand, 6 the multiplier, and $42 the product. The multiplier 6 is the sum of six l's, and the product 42 is the sum of six 7's. Hence, it will be seen that:

Multiplication is an operation by which, when two numbers are given, called multiplicand and multiplier, a third number is found called product, which is formed from the multiplicand as the multiplier is formed from unity.

52. The multiplicand is the number to be multiplied. The multiplier is the number by which we multiply. The product is the result obtained. The multiplicand and mul

tiplier are called factors of the product. The product of two or more factors is the same in whatever order they are taken. Thus, 3 × 4 = 4 x 3. The dots in the margin, read horizontally, make 3 fours; read vertically, make 4 threes.

53. The sign of multiplication is X. When the multiplier precedes the multiplicand, the sign X is read times. Thus, 6 x $7$42 is read 6 times $7 equal $42.

54. When the multiplier follows the multiplicand the sign X is read multiplied by. Thus, $7 × 6=$ 42 is read $7 multiplied by 6 equal $42; and means $7 taken ́ 6 times equal $42. In all cases the product refers to the same kind of units as the multiplicand.

55. Products of two factors, which are each less than ten, must be learned by heart.

They can all be readily found by addition. Thus, if the product of 4 times 6 is required, we see that the multiplier 4 is the sum of four 1's, and the multiplicand is 6; hence, the product is the sum of four 6's, and we write

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In the same way every product is found when each of its two factors is less than ten; and the results are all written in the following multiplication table:

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