77. There is a

kind of snail that has upon its tongue

160 rows of teeth, and 180 teeth in each row; how many teeth have 2 such snails?

78. If a machine can make 46 paper bags in a minute, how many paper bags can the same machine make in 2 hours of 60 minutes each ? Ans. 5,520 bags.

79. If 2760 bags can be made in one hour, how many can be made in 6 days of 11 hours each?

80. How much money does a person make in 12 weeks who gives 4 lectures a week, receiving 75 dollars more than his expenses for each lecture? Ans. 3,600 dollars.

81. In one year there are 8766 hours; how many hours has a boy lived who is 12 years old?

82. In one year there are 525960 minutes; how many minutes has a boy lived who is 15 years old?

83. If 15000 types can be set by one machine in one hour, how many can be set by 2 machines in 3 days of 9 hours each?

84. How much will a photographer receive for 42 dozen photographs at 3 dollars a dozen, and 5 photographs at 8 dollars apiece? Ans. 166 dollars.

85. How many days are there in 35 years of 365 days each, and 12 years of 366 days each?

86. Arthur sold 23 boxes of strawberries at 35 cents a box, and spent 500 cents of the money he received, for flour; how many cents had he left?

87. Mr. Lee owned 45 shares of railroad stock worth 100 dollars a share, 38 shares of the stock of a coal company worth 10 dollars a share, and enough real estate to make his entire property worth 14500 dollars; what was the worth of his real estate?

DIVISION.

86. If a boy has six tops and gives two of them away, and then another two, and then another two, how many twos of tops does he give away?

In this case, we find how many twos of tops there are in another number of tops, six.

The process of finding how many equal numbers, one of which is given, there are in another number, is Division. What is division?

87. In the above illustration, six tops is the number divided; the number divided is the dividend.

What is the dividend?

88. In the illustration, two tops is one of the equal numbers which there are in another number, six tops. Any one of the equal numbers which there are in another number is a divisor.

What is a divisor?

89. The result of division, or the number of equal parts obtained, is the quotient.

What is the quotient?

90. If in the above illustration the boy had had seven tops instead of six, and had given away twos of tops, as before, would he have had any tops left? How many

y?

The part of the dividend left after equal numbers are taken away, is the remainder.

What is the remainder?

91. The dividend may be regarded as a whole, of which it is required to find the number of equal parts, one of the equal parts being given.

The process of division may be thus expressed:

One of the equal

parts, called divisor. 2 tops,) 6 tops, {The whole number,

Number of equal parts there are

3 parts, in the whole, called quotient.

REMARK. - Division may be regarded as the reverse of multiplication; for, while in division the whole and one of the equal parts are given, and it is required to find the number of parts, in multiplication one of the equal parts and the number of parts are given, and it is required to find the whole.

92. The sign of division is a short horizontal line between two dots; thus, . The expression

62 3

shows that there are three 2's in 6. It may be read, "2's in 6, 3," or "6 divided by 2 equals 3."

NOTE. Sometimes the dividend and divisor are expressed in place of

read "1 half of 6 equals 3," or "6 divided by 2 equals 3."

TO THE TEACHER. As this form of expression is also used for fractions, it has been urged that its use in division should be discontinued ; but as it is a convenient form, and one extensively used, it is here retained. If the following could be universally adopted, it would, on some accounts, be preferable :

2|6
= 3.

93. ILLUSTRATIVE EXAMPLE I. Among how many pupils must 48 pencils be divided that each pupil may receive 2 pencils?

Explanation. — If each pupil receives 2 pencils, 48 pencils must be divided among as many pupils as there are 2's in 48.

We may ascertain how many 2's there are in 48 by taking away first one 2, and then another, and then another, till no 2's remain, and then counting the 2's taken; this is the method by subtraction. The following is the method by division:

:

OPERATION.

Units of pencils.

Tens

∞ Units

of pencils.

Divisor. 2) 4 8 Dividend.

Quotient. 24

Twos of pencils.

We express in figures the 48 with 2 at the left, drawing a curved line between the expressions and a straight line under that for the dividend.

48 equals 4 tens or 40, with 8.

In 40 there are twenty 2's, or 2 tens of 2's; we write a figure 2 under the line in the tens' place.

In 8 there are four 2's; we write a

figure 4 under the line in the units' place and have 2 tens with 4 units, or 24 for the result; therefore, that each pupil shall receive 2 pencils, 48 pencils must be divided among 24 pupils.

- In practice, the pupils need only say "2's in 4, 2; 2's in 8, 4:

OPERATION.

3) 246

82

How many 3's are there

Explanation. In the number 2 hundred there are no hundreds of 3's; we therefore first divide 24 tens.

In 24 tens, or 240, there are 80 threes, or 8 tens of 3's; we write a figure 8 under the line in the tens' place.

In 6 there are two 3's; we write a figure 2 under the line in the units' place, and have 82 for the quotient, which is the number of 3's in 246.

96. EXAMPLES.

5. A man has 306 quarts of milk which he wishes to put into cans that hold 6 quarts each; how many cans must he use? Ans. 51 cans.

6. In 420 days how many weeks?

Ans. 60 weeks.

7. In 1 peck there are 8 quarts; how many pecks are there in 488 quarts? Ans. 61 pecks.

8. A boy has 639 hours' work to do; how many days will it take him to do it, if he works 9 hours a day? Ans. 71 days.

97. ILLUSTRATIVE EXAMPLE III. At 8 cents apiece, how many oranges can be bought for 1945 cents?

OPERATION.

Thousands.

Hundreds.

Tens.

Units.

(16X32)

8) 1925
240

5

Explanation. As in 19 there are two 8's and 3 over, in 19 hundred there are 2 hundred 8's and 3 hundred over; we write a figure 2 below the line in the hundreds' place, and unite the 3 hundred which remain, with the tens, making 32 tens.

In 32 tens, or 320, there are 40 eights, or 4 tens of 8's; we write a figure 4 below the line in the tens' place.

In 5 there are no 8's; we write a zero in the units' place, and a figure 5 at the right to indicate the remainder.

NOTE. In practice, the pupil may say "8's in 19, 2 and 3 remain; 8's in 32, 4; 8's in 5 none, and 5 remain. Ans. 240 oranges; 5 cents remain."

98. PROOF.-Since the quotient shows how many parts equal to the divisor there are in the dividend, take the divisor for a multiplicand and the quotient for a multiplier, and to the product, when found, add the remainder if there is one. If the result is like the dividend, the work may be presumed to be correct.

99. EXAMPLES.

9. At 9 dollars a barrel for flour, how many barrels of flour can be bought for 200 dollars, and how many dollars Ans. 22 barrels; 2 dollars remair

will remain?