40. What decimal of a yard is of a yard? of a yard? 41. How may $ be expressed as the decimal of a dollar? 252. Analysis. — of a dollar equal 3 times of a dollar. Since 1 dollar is 100 cents, of a dollar is of 100 cents, and of a dollar are 3 times 25 cents, or 75 cents, or $.75. or 25 cents; Hence, etc. 42. In $3 how many cents? How many mills in of a cent? Express decimally the value of $5; $: $3. 3 6 43. Which term of a common fraction is the dividend? Which is the divisor? How is a common fraction changed to a decimal? 44. Since 10 mills are 1 cent, what part of a cent is 1 mill? 3 mills are what part of a cent? 5 mills? 7 mills? 45. Since 100 cents are 1 dollar, what part of a dollar is 1 cent? 5 cents are what part? 25 cents? 50 cents? 46. Since 1000 mills are 1 dollar, what part of a dollar is 1 mill? 7 mills are what part? 75 mills? 625 mills? 47. How many sheets of paper at 1 cent a sheet can be bought for $1? For $1.25? For $2.50? 48. How many bushels of apples at $1 a bushel can be bought for 500 cents? For 700 cents? For 800 cents? 49. By selling apples at 1 cent each, a boy took in 1 dollar 10 cents a day. How many apples did he sell? 50. At $1 each, how many books can I buy with 625 cents, and how many cents will I have left? 1212 100" 2009 51. At $.121⁄2 a pound, what will 12 pounds of sugar cost? 253. Analysis. -Since 1 pound costs $.12), or of a dollar, 12 pounds cost 12 times $3, or $12, or Hence, etc. or 25%, or $12, or $1.50. 52. At $.163 a yard, what will 8 yards of muslin cost? At $.25 a yard? At 333 cents a yard? 53. What is the cost of 10 pounds of flour at $.061 a pound? The cost of 12 pounds? Of 20 pounds? Of 32 pounds? 54. If 12 dozen eggs cost $2, what is the price per dozen? 254. Analysis. - Since 12 dozen eggs cost $2, the price per dozen is of $2, or † of $1, or $3, or $.163. Hence, etc. 55. If 16 pounds of mutton cost $2, what is the price per pound? If 16 pounds cost $3? If 20 pounds of beef cost $5? 56. If 24 quarts of berries cost $1.50, what is the price per quart? If they cost $2? If they cost $3? If $4? 57. If a piece of linen containing 12 yards cost $7.50, what was the price per yard? If 16 yards cost $9? 16% 50 58. At $.16% a yard, how many yards can be bought for $2? 255. Analysis. — Since 1 yard costs $.163, or or 300 or of a dollar, for $2 there can be bought as many yards as the number of times $ is contained in $2, or 12 yards. Hence, etc. 59. For $3 how many pounds of raisins can be bought at $.12 a pound? At $.20? At $.25? At $.33!? At $.37? 60. At $1.25 each, how many silk handkerchiefs can be bought for $5? For $7.50? For $10? For $12.50? 256. Principles. I. The value of a decimal is not changed by annexing ciphers to, or omitting ciphers from, the right of the decimal. II. A decimal fraction is a decimal with the denominator expressed. III. The value of a fraction is the quotient of the numerator divided by the denominator. Exercises. Tell, with your reason, how to express 1. .2 as hundredths; .4; .6. 4. $5 as cents. 7.75 cents as mills. 2. .25 as thousandths; .75. 5. $6.25 as mills. 8. 250 cents as dollars. 3. .700 as hundredths; as tenths. 6. $7.50 as cents. 9. 2006 mills as dol. Express 3.06 as a mixed fraction. 614 100, 257. Model. Since .06 is 6 hundredths, it may be expressed 25 which equals 55, or 1; and, united with the integer 3, gives 3 the mixed number required. 1 16 Express as fractions in their lowest terms, or as mixed numbers 258. Model. — equals 3 divided by 4; and since 1 is 10 tenths, 3 is 3 times 10 tenths, or 30 tenths. of 30 tenths is 7 tenths, with 2 tenths remaining. 2 tenths are 20 hundredths; of 20 hundredths is 5 hundredths. The result is 7 tenths 5 hundredths, or .75, which, united with the integer 4, gives 4.75, the mixed decimal required. 3. Applications of Decimals. 1. How many tenths are 3 tenths and 4 tenths? and ? 2. How many tenths are 8 tenths less 3 tenths? 3. What is the sum of and 7? Of 4 and .6? ΤΟ less 50 4. Find the difference between 8 and 3%. .9 and .4. 75 5. What is the sum of 1 and 25? The sum of .05 and .75? 6. Find the difference between 5 and 80. 1 and .75. 7. Find the sum of 18 and 15. The sum of .7 and .25. 8. What is the difference between and? .75 and .5? 9. How many hundredths and tenths in .07 and .18? 10. Find how many hundredths and tenths in .5 less .25. 11. What is the sum of 1%, Too, Too? Of .4, .6, and .008? 10 100, 12. How much is less 50? .06 less .006? .8 — .008? 13. What is the sum of 8 and expressed decimally? Of 12 and? Of 15 and .75? Of $8 and $1 ? Of $10 and $.75? 14. Find the difference between 7 and expressed decimally. Between 10 and .75. Between $8 and $3. Between $12 and $.25. Between $12.50 and $81%. 15. When only can integral units be added or subtracted? When only can fractions be added or subtracted? Decimal units? 16. How many decimal places in the sum of tenths and tenths? Of tenths and hundredths? Of hundredths and thousandths? Tenths and thousandths? 17. In the difference between tenths and hundredths, how many decimal places? Between hundredths and thousandths? Tenths and thousandths? 18. If a farmer sells .10 of a lot of wheat to one miller, and .25 to another, what part does he sell to both? 19. If I offer a $1 bill in payment for a pair of gloves that cost but $.75, how much change should I receive? 20. A gardener paid $1.50 for a spade, and $1.25 for a rake. How much did he pay for both? 21. If a lady pays $.25 for sugar, $.30 for coffee, and $.75 for tea, what does she pay for them all? 22. What is the remainder of $1 less ? $2 less $.061? 23. A carter bought a bushel of corn for $.871⁄2, and a bushel of oats for $.621. What did both cost him? 24. From a barrel of oil, containing 31.5 gallons, 4 gallons were drawn off. How many gallons remained? 25. What part of a dollar must be added to $9.99 to make $10? How much is 1 tenth less 1 thousandth? 26. What is the weight of three bars of silver weighing respectively .75 of a pound, 2.5 pounds, and .371⁄2 of a pound? 27. James had a five-dollar bill, and paid $2.25 for some books, and $2 for some paints. What had he remaining? 28. If I pay $6.50 for a barrel of flour, and $23 for groceries, what change from a $10 bill should I receive? 29. A silversmith had 12 ounces of silver, from which he made a set of teaspoons weighing 3.75 ounces, and a set of tablespoons weighing 7.5 ounces. How much had he left? 30. From a piece of carpeting containing 30 yards were sold one piece measuring 18.5 yards, and another measuring 8.25 yards. How many yards remained? Find the sum and the difference of 31. 8 yards and .25 of a yard. | 35. 5 bushels and 2.25 bushels. 32. 36 gallons and 1.5 gallons. 36. 10 feet and .621⁄2 of a foot. 33. 7.5 rods and 181 rods. 37. $10 and .87 of a dollar. 34. .37 of a dollar and $61. 88. 14.5 days and 12 days. 39. How many tenths are 2 times 4 tenths? 3 times? 40. How many tenths in of 4 tenths? 12 of? of.8? 41. How much is 3 times? 2 times .4? 4 times .5? 42. How much is of 116? of 35? of .64? 100 43. Find the product of 3 times; 4 times .06; 5 times.09. 44. What is the quotient of .25 divided by 5? 72 divided by 8? 8 divided by 4? .024 divided by 6? 45. What is the product of 46. Divide by 3%; 47. Multiply multiplied by? .4 × .4? 77% by 180; .9 by .3; .72 by .08. 72 by 2; 180 by ; .03 by .2; .03 by .02. 48. Divide 24 by 8; 24 by ; .24 by .8; .024 by .08. 49. Find the product of 5 times $.08; 9 times $.005. 50. How much is } of $24? of $.63? $.075 divided by 5? |