5.372 100 537.200 21. 578 by .0934. 22. 0.765 by .067. EXPLANATION. Since each removal of a figure one place to the left increases its value tenfold, the removal of the decimal point one place to the right multiplies by 10, and its removal two places to the right multiplies by 100; or, the process may be performed in the ordinary manner. 24. Multiply 27.65 by 10. 28. Multiply 6.8735 by 100. 25. Multiply 49.675 by 10. 29. Multiply .3768 by 1000. 26. Multiply 2.795 by 100. 30. Multiply 6.835 by 100. 27. Multiply 8.935 by 100. 31. Multiply .7634 by 1000. By 100. By 1000. By 10,000. 32. Multiply 89.92 by 10. 33. Multiply 68.3025 by 100. By 1000. By 10,000. 34. Which is larger and how much, the product of .625 and .375, or their sum? 35. What will 52.75 bushels of oats cost at $.45 per bushel? 36. A merchant sold 24.25 yards of muslin at $.125 a yard. How much did he receive for it? 37. A man bought 214 bags of barley. What did they cost him, if each bag held 2.5 bushels, and the price was $.96 a bushel ? 38. A tailor bought 4.5 yards of cassimere at $2.25 a yard, and 6.25 yards of broadcloth at $6.50 a yard. How much more did the broadcloth cost than the cassimere ? 39. How many acres are left in a farm of 563.27 acres, if 3 fields of 57.135 acres each are sold from it? 40. A steamship in crossing the Atlantic sailed at an average speed of 325.75 miles per day. If another steamer sailed from the same port at the same time at the rate of 395.35 miles per day, how far were they apart in 5.75 days? DIVISION OF DECIMALS. 193. 1. When a number is divided by 3, what part of it is found? By 6? 2. How much is 3. How much is 4. How much is 6)109.92 18.32 of 15? 15÷5? of .6? 1⁄2 of .6? of .24? † of .36? 194. 1. Find 1 sixth of 109.92, or divide 109.92 by 6. EXPLANATION. One sixth of 10 tens is 1 ten and 4 tens remaining; 1 sixth of 4 tens remaining and 9 units, or 49 units, is 8 units and 1 unit remaining; 1 sixth of 1 unit remaining and 9 tenths, or 19 tenths, is 3 tenths and 1 tenth remaining; 1 sixth of 1 tenth remaining and 2 hundredths, or 12 hundredths, is 2 hundredths. Therefore, one sixth of 109.92 is 18.32, or the quotient of 109.926 is 18.32. 2. What is 1 fifth of 86.4055 ? 5. $234.54÷9=? 6. $907.34 ÷ 7 = ? 3. What is 1 eighth of 94076.8 ? 4. What is 1 eleventh of 1086.415? 7. $324.784÷8=? 8. Find 1 eighth of 9675 acres. 8)9675.000 1209.375 EXPLANATION. - We divide as in simple division until we come to the remainder, 3 acres. This we change to 30 tenths and continue the division thus: 1 eighth of 30 tenths is 3 tenths and 6 tenths, or 60 hundredths, remainder. 1 eighth of 60 hundredths is 7 hundredths and 4 hundredths, or 40 thousandths, remainder; 1 eighth of 40 thousandths is 5 thousandths. Therefore, 1 eighth of 9675 acres is 1209.375 acres. 18. A man received $3278 for 5 acres of land. What was the price per acre? 19. An estate valued at $35,267 was divided equally among 8 children. What was each child's share? 195. The number of decimal places in the quotient. 1. What is the product of .5 x .7? How many decimal places does it contain? If.35 is divided by .7, what will the quotient be? How many decimal places does it contain? 2. What is the product of .9 x.05? If .045, the product, is divided by .9, one of the factors, what is the other factor? How many decimal places does it contain? 3. Since the product contains as many decimal places as there are in all the factors, if the product of two factors is given and one of the factors, how may the number of decimal places in the other factor be found? 4. Since the dividend may be regarded as the product of two factors, one of which is the divisor, and the other the quotient, how may the number of decimal places in the quotient be found from those in the dividend and divisor? 196. It is therefore evident that: The quotient will contain as many decimal places as the number of decimal places in the dividend exceeds the number in the divisor. WRITTEN EXERCISES. 197. 1. Divide .15652 by .043. .043).15652 (3.64 129 275 258 EXPLANATION. Since the dividend is equal to the product of the divisor and quotient, if 15652, the numerator of the dividend, is divided by 43, the numerator of the divisor, the result obtained will be the numerator of the quotient. Dividing, it is found to be 364. Hence, the numerator of the quotient is found precisely as in simple division. The denominator of the quotient may be found by dividing the denominator of the dividend by the denominator of the divisor, that is by dividing 100000 by 1000, which gives 100. Therefore, the quotient is 364, or 3.64. Or, 172 The quotient will contain as many decimal places as the number of decimal places in the dividend exceeds the number in the divisor. Art. 228. 198. Hence it is evident that: In dividing decimals, we divide as if the numbers were integers, and from the right of the quotient point off as many places for decimals as the number of decimal places in the dividend exceeds the number in the divisor. 1. If the quotient does not contain a sufficient number of decimal places, the deficiency must be supplied by prefixing ciphers. 2. Before commencing the division, the number of decimal places in the dividend should be made at least equal to the number of decimal places in the divisor. 3. When there is a remainder after using all the figures of the dividend, annex decimal ciphers and continue the division. 4. For business purposes, it is not necessary to carry the division further than to four or five decimal figures in the quotient. 9. .12376 by .0364. 10. .0184428 by .5123. 11. .29184 by .0057. 12. 4.5872 by .0122. 13. .056448 by 15.68. 14. .0816785 by 6.235. 15. .0983253 by .0673. 16. 5.97066 by 35.73. 32. Divide 325.47 by 100. 100)325.47 EXPLANATION. 3.2547 22. .07245 by .23. - Since each removal of a figure one place to the right decreases its value tenfold, the removal of the decimal point one place to the left divides by 10, and the removal two places by 100. 199. Hence it is evident that: To divide by 1 with any number of ciphers annexed, the decimal point should be removed as many places to the left as there are ciphers annexed to the 1. 39. How many yards of cloth, at $ 5.75 per yard, can be bought for $153.525 ? 40. How many barrels of apples, at $ 1.25 per barrel, can be bought for $18.43 ? 41. How many cords of wood, at $ 5.62 per cord, can be bought for $1495.12 ? ACCOUNTS AND BILLS. 200. A record of the debts and credits between two parties is called an Account. 201. A statement of the quantity and price of the articles sold, and the value of the whole, is called a Bill. A bill is receipted when the words Received Payment, or Paid, are written at the bottom, and the seller's name is signed either by himself or by some authorized person. 202. The following abbreviations are in common use: |
