38. If a boy rides 233 mi. on a bicycle in 24 hr., what is his rate per hour?

39. In buying 2 doz. cans of peaches, how much is gained by buying @ $3.74 a dozen over buying at the rate of 3 cans for a dollar?

40. What is the cost of 64 lb. of mackerel @ 16, 3 lb. of codfish @ 12, and 4 cans of salmon at the rate of 2 cans for a quarter?

41. I bought gal. of olive oil @ $3.30 a gallon, but of what I bought leaked out. What rate per gallon do I pay for what is left?

42. In buying 48 cans of tomatoes, how much is gained by buying two cases of 2 doz. each, @ $2.89 a case, over buying at the rate of 3 cans for 40¢?

43. I bought 3 gal. of best maple sirup @ $1.12 a gallon, and 2 gal. of New Orleans molasses @ 62 a gallon, and gave the grocer a $5 bill. How much change did I receive? (Neglect fractions less than 1, although in a bill a fraction of a cent is usually called a cent.)

44. I bought 8 lb. of prunes @ 121, 4 lb. of figs @ 199, 21 lb. of candles @ 121, 12 lb. of sugar @ 64, and 24 lb. of English walnuts @ 18, and gave the grocer a $5 bill. How much change did I receive?

45. I bought 10 lb. of white beans @ 617, 31 lb. of split peas @ 74, 3 cans of soup @ 121, and 21 lb. of paraffin candles@12. How much was my bill?

46. If we buy 12 lb. of sugar at 53, 31 lb. of tea at 60%, and 12 lb. of coffee at 37, how much is the bill?

47. If 12 cups of flour make 4 loaves of bread, how many loaves will a barrel of flour make? Allow 3 cups of flour to the pound, and 196 lb. of flour to the barrel.

48. If a recipe will provide enough for 5 persons, and you wish to provide for 8 persons, what part must you add to the recipe? Instead of 10 teaspoons you would need how many?

49. Providing 1 potatoes for each person at a meal, how many potatoes would you need for 8 persons?

50. If there are 40 potatoes in a peck, and you use 12 of them, what fractional part of a peck do you use?

51. If a family uses of a peck of potatoes in one day, how many pecks will it use in a month of 30 days?

52. Allowing 4 cups to the quart, a quart of cranberries divided among 16 pupils in a class would allow what part of a cup to each member?

53. Cranberries are cooked with half as many cups of sugar as of berries, and half as many cups of water as of sugar. If you wish to cook 3 pt. of cranberries, how much sugar will you use? How much water?

54. If flour costs $6.25 a barrel (196 lb.), or 31 a pound when bought by the pound, how much is saved on 196 lb. of flour in buying by the barrel?

55. If a family uses 12 cups of flour in each baking of bread, and there are 2 bakings a week, and we allow 4 lb. to the cup, how many pounds of flour would be used in a year?

56. If we pay 25g for a box of domino sugar weighing 3 lb., how much do we pay per pound?

57. A gallon of water contains 231 cu. in., and 1 cu. ft. of water weighs 62 lb. If the water in a tank weighs 14,437 lb., how many gallons are there?

On pages 226-230 many industrial problems are included, requiring the use of denominate numbers and fractions, as suggested by the New York State Syllabus. If further work of this nature is needed at this time, pages 99-142 may be reviewed in whole or in part.

CHAPTER XI

PERCENTAGE

217. Per Cent. Another name for hundredths is

per cent. ʊ, is

of

Thus 0.01, or ro, is the same as 1 per cent; 0.00, or the same as per cent; 0.06 is the same as 6 per cent. That part of arithmetic which treats of per cent is called percentage.

218. Symbol for Per Cent. The symbol for per cent is written thus: %.

We may read 0.06 either " 6 hundredths or 6 per cent." In the same way, we may think of 6% as either 6 per cent" or "6 hundredths," although it is read "6 per cent."

The expression 800% means 88 and equals the whole number 8; 225% equals the mixed number 2.25, or 24; 1% means

zʊ, and is read either "per cent " or, quite commonly,"

of ro, or of 1%."

219. Relation to Fractions. Since 6% means 180, which equals 0.06, or, we see that we may express per cent as a decimal fraction or as a common fraction.

It is often convenient to use one form, and often another. Thus, if we are multiplying by 13.5%, it is more convenient to think of the multiplier as 0.135; but if we are multiplying by 331%, it is better to think of it as instead of 0.33}.

220. Per Cents as Common Fractions. Since 62%

621

100

=

To express per cent as a common fraction, write the number indicating the per cent for the numerator and 100 for the denominator, and reduce this fraction to lowest terms.

For example, 50% means 0.50, or 50%, and this equals. Likewise, 25% means 0.25, or 125, and this equals 1.

EXERCISE 125

Reduce to a common fraction, integer, or mixed number:

To express as a decimal a number written with the per cent sign, omit the sign and move the decimal point two places to the left.

=

Thus 11% 0.011, or 0.015; 125% = 1.25; 0.6% = 0.006.

80% of 90?

80% of 900?

Since 25.5% and 0.255 have

222. Decimals as Per Cents. Since per cent means hundredths, to express a decimal as per cent we have to consider only how many hundredths the decimal represents.

Thus

0.3 0.30 30 hundredths = 30%.

=

=

0.375 = 0.371 = 371 hundredths = 371%, or 37.5%.

==

1.25 = 135 = 125%.

Therefore, to express a decimal as per cent, write the per cent sign after the number of hundredths.

11. A pint is what per cent of a quart? of a gallon? 12. A dime is what per cent of a dollar? of a cent?

223. Common Fractions as Per Cents. Since per cent means hundredths, therefore

To express a common fraction as per cent, reduce it to hundredths, omit the denominator, and write the numerator followed by the per cent sign.

This is easily done by reducing the common fraction to a decimal and proceeding as in § 222.

11. A foot is what per cent of a yard? of 2 yards?

12. An ounce is what per cent of a pound? of 2 pounds?