Since 8 is of 100, multiply 62 by 12, and divide the product by 100.

124. 1. In the year 1882 Pennsylvania raised 43,518,800 bushels of corn. At an average yieli of 32 bushels an acre, how many acres were planted in corn ?

2. In the same year, Illinois raised 182,336,900 bushels of corn, on 7,914,042 acres. What was the average yield per acre? Disregard fractions.

3. The population of the United States was, in 1800, 5,308,483; in 1880, it was 50,155,783. What was the average annual increase? Disregard fractions.

4. The settled area of the United States in 1880 was 1,569,570 square miles; the population was 50,155,783. What was the average number of persons to a square mile? Disregard fractions.

5. The population of Belgium is 5,253,821; its area 11373 square miles. What is the average population

to the square mile ?

SUMMARY.

125. Division is a process of finding how many times one number is contained in another; or, Division is a pro

cess of separating a number into equal parts.

126. The Dividend is the number to be divided.

127.

The Divisor is the number by which the Dividend is to be divided.

128. The Quotient is the result obtained by Division. It shows how many times the Divisor is contained in the Dividend.

129. The Remainder is that part of the Dividend remaining undivided.

130. The Sign of Division is +.

13I.

A Dividend is the product of its Divisor and Quotient. Division is thus the converse of Multiplication. Multiplication is the process of finding the product when its two factors are given. Division is the process of finding the other factor when the product and one of the factors are given. Division is thus a "proof" of Multiplication, and Multiplication is a proof of Division.

132. The removal of the decimal point one place to the left, divides a number by ten.

133. For additional examples in Division, use Article 110. Divide each number in column A. by the corresponding number in column B, etc. Thus, 25596÷46 ; etc.

Article 134.

CHAPTER VI.

SOME GENERAL PRINCIPLES.

I. The whole is equal to the sum of all its parts.

1. A boy's library consists of 12 volumes of fiction, 8 volumes of poetry, 20 volumes of history, and 25 volumes on miscellaneous subjects. How many volumes does he have in all?

2. A regiment of 900 men are quartered as follows: 200 at A, 300 at B, the others at C. How many men are at C ?

II. The greater of two numbers is equal to the less plus their difference.

III. The less of two numbers is equal to the greater,
minus their difference.

3. Henry walked 23 miles, a distance 7 miles greater than
John walked. How many miles did John walk ?
4. The difference of the ages of Mary and Ruth is 5
years. Ruth is 12 years old; how old is Mary?

IV. The greater of two numbers is equal to one half their
sum plus their difference.

V. The less of two numbers is equal to one half their sum less their difference.

VI. The sum of two numbers is equal to twice the less

number plus their difference.

S=21+d.

5. The sum of two numbers is 12; their difference is 2; what are the numbers ?

6. The sum of two numbers is 24; their difference is 8; what are the numbers ?

7. The less of two numbers is 15; their difference is 6; what are the numbers ?

VII. The multiplication or division of either factor of a product, by any number, multiplies or divides the product by that number.

8. Mr. A. gave 3 pears to each of 4 boys. How many pears did he give to all? If he had given 6 pears to each boy, how many pears would he have given to all? If he had given 3 pears to each of 2 boys, how many pears would he have given to all?

VIII. The multiplication or division of a dividend by any number, multiplies or divides the quotient by that number.

9. 48 dollars are to be divided among 6 men; how many dollars will each man receive ? If one half as many dollars, 24, be divided among the same number of men, how many dollars will each receive ?

IX. The multiplication of a divisor by any number divides the quotient by that number; the division of a divisor by any number multiplies the quotient by that number.

10. 40 bushels of potatoes were divided equally among 4

families; how many bushels did each receive? If the same number of bushels had been divided among 8 families, how many bushels would each have received? If among two families?

X. The multiplication or division of both dividend and divisor by the same number does not change the quo

11. 50 dollars are divided equally among 5 men; how many dollars does each man receive? 500 dollars are divided equally among 50 men; how many dollars does each man receive? How do they compare? How do they compare ?

What are the two dividends? What are the two divisors ? What is the quotient in each?

REVIEW PROBLEMS.

135. 1. The area of Illinois is 610 square miles greater than the area of Wisconsin. Together these two states contain 112690 square miles. What is the area of each? 2. The area of Palestine was probably 9840 square miles, which is 275 square miles more than the area of Vermont. How many square miles has Vermont ? 3. Of the 444,027 immigrants who arrived in the United States in the year 1889, 153,549 came from the British Isles, 279,270 from Continental Europe, 1725 from Asia, 81 from Africa, the others from other countries. How many came from other countries ?

4. The sum of 3 numbers is 847960; one of the numbers is 275406; the other two are equal; what are they? 5. The quotient is 784, the remainder is 75, the divisor is 256. What is the dividend ?

6. One half the sum of two numbers is 896; one half their difference is 87. What are the numbers ?

7. The product is 876158; the multiplier is 562; what is the multiplicand?

8. The quotient is of the dividend which is 968127; what is the divisor?

9. A merchant bought 125 barrels of flour at $5 a barrel, and 28 barrels of sugar at $18 a barrel. How many dollars did he pay for all?