67. To multiply by 13, 14, 15, 16, 17, etc. : RULE. Multiply by the right-hand figure of the multiplier, set the product under the multiplicand, ONE PLACE FUrther to THE RIGHT, and add. 81. Multiply 426 by 17. OPERATION. 426 2982 7 2 4 2, Ans. The 2982 is 7 times 426, and the 426, standing one place further to the left, is 10 times 426 (Art. 15), .. their sum is 17 times 426. 82. Multiply 342 by 18. By 14. By 16. In a similar manner multiply by 102, 1005, 10009, etc. 83. Multiply 2463 by 102. 84. Multiply 3248 by 104. By 1004. By 1008. 63. To multiply by 21, 31, etc.: RULE. Multiply by the left-hand figure of the multiplier, set the product under the multiplicand, ONE PLACE FURTHER TO THE LEFT, and add. 36. Multiply 34264 by 81. By 41. By 61. In like manner multiply by 201, 301, 6001, etc. 87. Multiply 4237 by 501. Ans. 2122737. 88. Multiply 34265 by 801. By 4001. By 30001. 67. To multiply by 13? By 15? By 102? By 1005? Reason? 68. To multiply by 21? By 81? By 501? Reason? Why better than the common method? MISCELLANEOUS EXAMPLES IN MULTIPLICATION. 1. What cost 11 pounds of beef at 9 cents per pound? Ans. 99 cents. 2. What cost 98 tons of hay at $15 per ton? Ans. $1470. 3. In one hogshead of wine are 63 gallons; how many gallons in 75 hogsheads? 4. In a certain house are 75 rooms, in each room four windows, and in each window 12 panes of glass; how many panes of glass in the house? 5. The earth, in its annual revolution, moves 19 miles in a second; how far will it move in an hour, there being 60 seconds in a minute, and 60 minutes in an hour? 6. Light moves 192000 miles in a second; how far will it move in an hour? 7. How many yards of cloth in 10 bales, each bale containing 25 pieces, and each piece 24 yards? 8. If 12 men do a piece of work in 7 days, in how many days can 1 man do 5 times as much work? 9. Multiply forty-three million, seven hundred and four thousand, eight hundred and sixteen, by forty-two thousand and eight. 10. A man bought 24 city lots at $365 each; what did they all cost him? 11. Multiplicand 4632; multiplier = 4008; product? 4444; product=? EXAMPLES IN the ForegoING PRINCIPLES. 1. Two men start from the same place, and travel in the same direction, one at the rate of 56 miles and the other 75 miles per day, how far apart are they at the end of 43 days? 2. Had the men named in Ex. 1 traveled in opposite directions, how far apart would they have been in 56 days? 3. Bought 58 tons of hay for $600 and sold it for $12 per ton; did I gain or lose? How much? 4. Bought 25 horses for $125 each, and 14 pairs of oxen, at $87 a pair; what did I pay for all? 5. Bought 56 barrels of flour at $9 per barrel, and in pay for it gave 48 cords of wood at $6 per cord, and the rest in money; how much money did I pay? 6. Paid $7 each for 63 sheep, and sold the flock for $425; did I gain or lose? How much? 7. A farmer sold 56 bushels of wheat at $2 per bushel, for which he received 40 yards of cloth at $2 per yard, and the balance in money; how much money did he receive? 8. A merchant bought 846 barrels of flour for $7191; he sold 526 barrels at $9 per barrel, and the remainder at $8 per barrel; did he gain or lose? How much? Ans. Gained $103. 9. A man's income is $1575 a year, and his expenses are $3 a day; what does he save in a year of 365 days? Ans. $480. 10. Bought 18 tons of iron at $39 a ton, and 27 tons at $41; what shall I gain by selling the whole at $43 a ton? 11. A drover bought a herd of 33 oxen, paying as many dollars for each ox as there were oxen in the herd. He paid $500 in money, and gave his note for the balance; what was the size of the note? × 12. How many are 8+ (2 x 7) — (3 × 5) ? 13. How many are (9 × 7) + (3 × 5) — 12? 4? · (3 × 6) · 15. The factors of one number are 20, 14, and Ans. 7. Ans. 66. Ans. 26. 23, and of another 16, 8, and 7; what is the difference of the two numbers? Ans. 5544. 16. The President of the United States receives a salary of $25000 a year; what will he save in a year of 365 days, if his expenses are $50 a day? 17. A man having a journey of 313 miles to perform in 6 days, travels 54 miles a day for 5 days; how far must he go on the sixth day? 18. A many sold three farms; for the first he received $3475, for the second, $925 less than for the first, and for the third, he received twice as much as for the other two; how much did he receive for the three farms? 19. What shall I pay for 25 horses, at $75 each, and 12 oxen, at $54 each? 20. If a teacher receives a salary of $800 a year, and paya $210 a year for board, $75 for clothing, $50 for books, and $100 for other expenses, how much will he save in 3 years? DIVISION. 69. DIVISION is the process of finding how many times one number is contained in another. The DIVIDEND is the number to be divided. The DIVISOR is the number by which to divide. The QUOTIENT is the number of times the dividend contains the divisor. If the dividend does not contain the divisor an exact number of times, the part of the dividend which is left is called the REMAINDER. NOTE. The remainder is always of the same kind as the dividend, because it is a part of the dividend. Ex. 1. How many oranges, at 4 cents each, can be bought for 12 cents? Ans. As many oranges as there are times 4 cents in 12 cents; 4 cents are contained in 12 cents, 3 times; .. 3 oranges, at 4 cents each, can be bought for 12 cents. 2. How many apples, at 2 cents each, can be bought for 10 cents? Ans. As many as there are times 2 cents in 10 cents, or as there are times 2 in 10, viz. 5. 70. The sign of division, ÷, indicates that the number before it is to be divided by the number after it; thus, 8 ÷ 2 = 4, i. e. 8 divided by 2 equals 4, or 2 in 8, 4 times. 3. How many are 6 ÷ 2? Ans. 2 in 6, 3 times. 69. What is Division? What the Dividend? Divisor? Quotient? Remainder? Of what kind is the remainder? 70. The sign of Division, what does it indicate? |