FOR WRITTEN SOLUTION.

59. 1. Harry paid $ for a knife, for a book, and $1 for a necktie. What did he pay for all?

WRITTEN SOLUTION. $+$+$1 = what he paid for all.

ORAL SOLUTION. He paid the sum of $3, $, and $1, which is $11. 2. A grocer sells of a box of tea from a box full. What part of the whole box is left?

ORAL. There was left the difference between & and §, which is . 3. If a man earn $2 a day, what will he earn in 6 days? WRITTEN. $1% 6 what he will earn in 6 days.

ORAL. He will earn 6 times $1, or $53, equal to $5.

4. If of a barrel of flour is divided equally among 3 poor 용

families, what part of a barrel will each receive?

WRITTEN. bbl.÷3, or of

what each will receive.

ORAL. Each family will receive } of § bbl., or of a barrel of flour. 5. If a man earns $15 a week, and spends of it, how much does he save ?

6. If 3 oranges are worth of a melon, what part of the melon is 1 orange worth?

7. Rollin had 18 marbles, and gave of them to Martin. How many marbles did he give Martin, and how many did he keep for himself?

8. Andrew is 18 years old, and his sister Jane is as old. How old is Jane?

9. Paid $36 for 1 acre of land. What is of it worth? j? ? ?

10. If 1 man consume of a pound of meat in a day, how many pounds would 6 men consume?

11. Oliver having 20 qt. of blueberries, sold of them for $. What was that a quart?

20.

DECIMALS.

60. The numbers 1000, 100, 10, 1, 1, 1, 1ooo, etc., in

crease from right to left, and the same uniform scale of ten.

decrease from left to right, by

Thus, 1000 is ten times 100;

is

100 is 10 times 10; 10 is ten times 1; 1 is ten times, etc. Also, Too is one tenth of 10; 1 is one tenth of; one tenth of 1; 1 is one tenth of 10, etc. The value of any

61. Decimal fractions may be written in two ways; either as other fractions, the denominator being expressed, or in decimal notation, the denominator being omitted. Thus,

The name of the first order at the right of units is tenths;

of the second, hundredths; of the third, thousandths.

62. The unit is the standard by which we compare all numbers. Therefore, to determine the order of units at a glance, a point is placed on the right of the order of units, and before the order of tenths.

It is written thus, (.), and is called the decimal point. Its only purpose is to determine the place of the order of units, and it must never be omitted.

Thus, in the number 62.55, the point shows the order of units, 2; and as we read sixty-two units, so we read fifty-five hundredths, giving to it the name of the lowest order.

63. When an integer and decimal are written together, the expression is a mixed number (52, 4).

Mixed numbers involving decimals are read in the same manner as mixed numbers involving common fractions.

Thus, .07 is read seven hundredths, .58 is read fifty-eight hundredths, 25.34 is read, twenty-five and thirty-four hundredths.

64. The relation of decimals and integers is clearly shown in the following Table:

Read as follows, always using the word "and" between the integer and decimal:

425 and 37 hundredths. 1046 and 65 thousandths. 32400 and 456 thousandths.

87 and 75 ten-thousandths.

4328 and 169 thousandths. 7000 and 7 ten-thousandths.

Ten-thousands.

Thousands.

Hundreds.

Tens.

UNITS.

Tenths.

Hundredths.

Thousandths.

Ten-thousandths.

65. Read the following numbers, naming all the orders, until the names of the decimal orders are as familiar as those

Additional examples may be given, at the option of the teacher.

DRILL EXERCISES.

66. 1. Express in decimal form 8. Ans. 18.09.

ORAL SOLUTION. The numerator is 9, the denominator 100; the decimal is expressed by a point, naught, nine; thus, .09, and is read nine hundredths.

The teacher should exercise the class orally by rapidly dictating similar examples, thus: "The denominator is 100, the numerator 5; what will express the decimal?" The prompt response should be, "Point, naught, five, read five hundredths" (.05).

Ques. "The denominator is 1000, the numerator 26 ?"

Ans. "Point, naught, two, six, read twenty-six thousandths" (.026).

67. 1. Express in form of a common fraction .09.

Ans. .09 180.

ORAL SOLUTION. The numerator is 9, the denominator 100, and the fraction is 80.

In like manner analyze and express,

Oral exercises similar to the following should be freely used. The teacher pronounces distinctly," Point, naught, five." The pupil promptly responds, "The numerator is five, the denominator one hundred, and the fraction is five hundredths" (150).

Ques. "Point, naught, two, six?" Ans. "The numerator is twentysix, the denominator one thousand, and the fraction is twenty-six thousandths" (1886).

1

ADDITION AND SUBTRACTION.

INDUCTIVE EXERCISES.

68. 1. What is the sum of 3 tenths and 6 tenths? and? Of.6 and .4? Of .3, .4, and .5?

Off

2. What is the difference between 7 tenths and 4 tenths? Between 12 hundredths and 8 hundredths?

3. What is the difference between and ? 7 and .4? 15 and 12? .15 and .11?

100

4. What is the sum of 8 tenths and 3 tenths? The difference?

5. What is the sum and difference of .07 and .12?

6. From

take. From .36 take .12.

7. From 1 take 10. From .028 take .010.

8. What is the sum of .12 and .20? .15 and .25? ·