3. What is the product of 0 × 180 ? Of .5 x .11 ? Of .03 × .12 ? 4. What is the product of × 10? 5. What is the product of×1000? Of .15 ×.006? WRITTEN EXERCISES. 1. Multiply .248 by .36. Process. .248 .36 1488 744 .08928 Analysis. Since multiplying thousandths by hundredths gives hundred-thousandths, the product is 8928 hundred-thousandths, or .08928. It is seen that the decimal places in the product equal the number in the multiplicand and multiplier. The same result may be shown thus: 1888 × 138 = 189880.08928. 248 ART. 177.-Rule for Multiplication of Decimals.-Multiply as in whole numbers, and point off as many decimal places in the product as there are in the multiplicand and multiplier. In case there are not the required number of decimal places in the product, prefix as many ciphers as are necessary to make the required number. Multiply: 2. 25.05 by .25. 3. 4.003 by .36. 4. 74.74 by .0009. 5. 384.31 by .64. 6. 78.78 by 78.7. 7. 320.32 by .3001. 8. .584 by 1. 9. 38.62 by 10. 10. 380.37 by 101 11. 6361.01 by .3. 12. 10000 by .001. . 13. 742.303 by 6. 24. .0325 by 25. 27. 17.20 by .20. 28. 2400 by 1.1. 29. .3 by .0008. 25. 1.017 by 1.2. 26. 23.07 by 3.08. 30. What is the value of 123 acres of land at $113.75 an acre? 31. What is the cost of 29.5 pounds of sugar at $.0625 a pound? 32. What is the value of 38 barrels of apples at $4.50 a barrel ? 33. The purchases made by a lady were: 23 yards of calico at $.08, 12 yards of gingham at $.10, 11 yards of muslin at $.12, 24 yards of drilling at $.115: what was the total cost of her purchases? 34. Illustrate by an original problem multiplication of decimals. Division of Decimals. ART. 178.-1. What is the product of .4 x .6? 2. What is the quotient of 2.4 ÷ 6? 3. What is the product of .5 × .7? WRITTEN EXERCISES. 1. Divide 15.424 by 3.2. Process. 3.2)15.424(4.82 12.8 262 256 64 ART. 179.-Rule for Division of Decimals.-Divide as in whole numbers, and point off as many decimal places in the quotient as the number of decimal places in the dividend exceeds the number in the divisor. NOTE.-When the dividend has fewer decimal places than the divisor, annex enough ciphers to the dividend to make them equal. When the number of quotient figures is less than the excess of decimal places in the dividend over those in the divisor, prefix as many ciphers as there are places lacking. 18. At $6.35 a ton, how many tons of coal can be bought for $76.20? 19. Illustrate by an original problem division of decimals. ART. 180.-To find the cost when the quantity and the price of 100 or 1000 are given. 1. If the cost of 100 articles is given, how can you find the cost of 200? Of 500? Of 800? Of 900 ? 2. If the cost of 100 articles is given, how can you find the cost of 250 ? 350? 375? 550? 575 ? 3. How many times 100 is 200? 225 ? 4. How many times 1000 is 5000 ? 5900? 5950? 600? 625 ? 250 ? 275 ? 5500 ? 5800 ? WRITTEN EXERCISES. 1. What is the cost of 550 pounds of plaster at $4.25 per 100 pounds. Process. $4.25 5.50 21250 2125 Analysis. Since 100 pounds cost $4.25, 550 pounds, or 5.50 times 100 pounds cost 5.50 times $4.25 or $23.375. $23.3750 NOTE.-The letters C. and M. respectively represent the words hundred and thousand. ART. 181.-Rule to find the cost, when the quantity and the price of 100 or 1000 are given.-Point off two places for price per hundred, or three places for price per thousand, and multiply the price by the quantity. 2. What is the cost of 15,500 shingles @ $5.75 per M.? 3. What is the cost of 8,548 feet of scantling @ $4.25 per M.? 4. I paid $6.25 per M. for 16,850 bricks: what was the cost? 5. A compositor was paid 48 cents per thousand ems for setting a book of 256 pages of 1,040 ems each: how much was he paid? 6. What is the cost of 1,275 bananas @ $2.25 per C.? 7. What must I pay for 780 envelopes @ $2.04 per C.? 8. What are 1,333 pine-apples worth @ $68.50 per M.? 9. A paid $1.75 per C. for 1849 feet of boards: what was the cost? 10. What is the cost of 1,960 pounds of hay @ $16.50 per ton (2,000 pounds)? United States Money. ART. 182.-United States Money is based on the decimal system. Calculations involving United States Money are performed in the same manner as in whole numbers and decimals. ART. 183.-The dollar is the unit; the dime is one tenth of a dollar; the cent one tenth of a dime, and the mill one tenth of a cent. There is no coin known as the mill; it is used only in making calculations. 10 mills (m.) = 1 cent, ct. 10 cents = 1 dime, d. 10 dimes = 1 dollar, $. The demands of business have compelled the subdivision of coins, so tnat those now used are: Bronze, 1 ct. and 2 ct. pieces; Nickel, 3 ct. and 5 ct. pieces; Silver, 5 ct., 10 ct., 25 ct., 50 ct., and $1 pieces; Gold, $1, $2, $5, $10, and $20. Some of the branch mints have coined 50 ct. and 25 ct. pieces of gold, but such coinage is illegal. The $10 piece is the eagle, the $5 piece the half eagle, and the $2 piece the quarter eagle. Paper money consists of bills of the denominations of $1, $2, $5, $10, $20, $50, $100, $500, and $1,000. Write: 1. Fifty dollars fifty cents. 2. Fifty-five dollars fifty-five cents five mills. 3. Seventy dollars eight cents six mills. 4. One hundred dollars three cents. |