56. Mr. Homer has 10 acres of wheat, 63 acres of corn, 20 acres of barley, and 16g acres of rye. How many acres of grain has he?

57. What is the quotient of 389 divided by 1556, expressed in its simplest form?

61. The product of two factors is 101; one factor is 3§. What is the other?

62. +64 +93 + 12 +16=?

63. (1 of 21 of 17) × (3 of 34 of 8 × }) = ?

64. The sum of two numbers is 1941. One of the numbers is 12%. What is the other?

68. A can do a piece of work in 4 days, B can do the same work in 5 days, and C in 6 days. In what time can all do it together?

69. A tank has 3 supply pipes. It can be filled in 6 hours by the first pipe, in 7 hours by the second, and in 8 hours by the third. In how many hours can the tank be filled by the three pipes together?

70. A and B can do a piece of work in 3 days. A can do it alone in 5 days. In what time can B do it alone?

SOLUTION. -Both can do of it in 1 day. A, alone, can do of it in 1 day. = 3, the part A can do in 1 day. Since he can of it in a day, he can do 33, or the whole of it, in as many days is contained times in 33, or 33 ÷ 5 = 63 days.

do

as

71. of my property is invested in land, of the remainder in business, and of the remainder, which is $2400, is in the bank. How much property have I?

72. What is the value of (13+ 6 − ‡ of § + 1) + 3 } ?

12

73. A farmer sold 11 doz. eggs at 141 a dozen, and took his pay in sugar at 51 a pound. How much did he receive?

had $2.25 left. How much did he pay for the knife?

76. A father left $ 39,000 to his two children, dividing it so that the daughter received as much as the son. was the share of each ?

What

77. A person owning of a steamboat, sold of his share for $17360. What was the value of the boat?

78. After spending of my money and of the remainder I had $300 left. How much had I at first?

79. If of of a bushel of apples cost of of a dollar, what will of § of a bushel cost?

80. How many pounds of honey at of of a dollar a pound can be bought for of 2 dollars?

DECIMAL FRACTIONS.

5 × 5 = 25,

138. A Power is the product of equal factors, as 5 × 5 × 5 = 125. 25 is the second power of 5. 125 is the third power of 5. 10 x 10 = 100. 10 x 10 x 10 = 1000. 100 is the second power of 10. 1000 is the third power of 10.

139. A Decimal Fraction or Decimal is a fraction whose denominator is 10 or a power of 10.

NOTE. The denominator of a common fraction may be any number, but the denominator of a decimal fraction must be 10, 100, or 1000, etc.

140. A decimal is written at the right of a period (.) called the Decimal Point.

NOTE. It is not customary to write the denominator of a decimal. It is determined by the position of the decimal point.

141. A figure at the right of a decimal point is called a Decimal Figure. Tenths are written like dimes with one decimal figure; thus, 5.5. Hundredths are written like cents, with two decimal figures; thus, 25 = .25, 17。 = .07. Thousands are written like mills, with three decimal figures; thus, 125.125, 18.016, 10.004. Ten-thousandths require four decimal figures; hundred-thousandths, five; millionths, six; etc.

142. Name the denominators in the following: .36; .08; .294; .1406: .0001; .263402.

Change to decimals:

1000; 10000

36

25 125; 100; 1000; 100000; 1000000;

143. A Mixed Decimal is an integer and a decimal; as, 16.04.

144. To read a decimal.

Rule. Read the decimal as an integer, and give it the denomination of the right-hand figure.

Rule. Write the numerator, prefixing ciphers when necessary

to express the denominator, and place the point at the left.

NOTE. There must be as many decimal places in the decimal as there are ciphers in the denominator.

Express decimally:

22. Four tenths. Seventeen hundredths. Five hundredths. Three hundred twenty-five thousandths. Five thousandths. Fifteen thousandths. Nineteen and seven

hundred twenty-four thousandths.

23. Seven thousand five hundred four ten-thousandths. Sixteen, and 125 ten-thousandths. Six ten-thousandths. Five thousand ten-thousandths.

24. Seventeen thousand two hundred eleven hundredthousandths. Four hundred-thousandths. Fifteen hundred-thousandths. Eighteen, and two hundred sixteen hundred-thousandths. One hundred twelve hundred-thou

sandths.

25. Twenty-nine hundredths. Twenty-nine thousandths. Twenty-nine ten-thousandths. Twenty-nine hundred-thousandths. One and one tenth. One and one hundredth. One and one thousandth. One and one ten-thousandth.

One and one hundred-thousandth.

26. 324 and one hundred twenty-six millionths. 4582 and 36242 hundred-thousandths. Seventeen millionths. Five hundred-thousandths. Twenty-four, and three thousand four hundred six ten-millionths.

27. 10 millionths. 824 ten-thousandths. 31 hundredths. 216 hundred-thousandths. 7846 hundred-millionths. Four and 15 hundred-thousandths.

146. PRINCIPLES. — Ciphers annexed to decimals do not change their value.

For each cipher prefixed to a decimal, the value is diminished tenfold.

The denominator of a decimal when expressed is always 1 with as many ciphers as there are decimal places in the decimal.

147. To reduce two or more decimals to a Common Denominator.

Rule.

Annex ciphers so that each decimal will have the same number of decimal figures.