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109. How many meters in 48 bales of goods, each bale containing 34 pieces, and each piece 37 meters?

110. How many miles will an engine run in 7 days if it runs 20 miles an hour and 15 hours each day?

111. A farmer had 23 acres of corn that yielded 49 bushels to the acre. How much is his corn worth at $0.75 a bushel?

112. Miss F., a teacher, pays $6 a week for her board for the 40 weeks of school, $10 a week for the 12 weeks of vacation, and for other expenses for the year $153. How much can she save in 7 years if her salary is $ 650 for the first three years and $750 for the last four years?

113. A farmer sold 56 hektoliters of wheat at $5 a hektoliter, and received 40 meters of cloth at $2.50 a meter. is the balance still due him?

What

114. If I buy 18 tons of iron at $39.25 a ton, and 27 tons at $ 41.75 a ton, what shall I gain by selling the whole at $43.25 a ton?

115. A drover bought a drove of 33 oxen, paying as many dollars for each ox as there were oxen in the drove. He paid $514.85, and gave his note for the balance. For how much does he give his note?

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53. What is Multiplication? 54. What is the Multiplicand? Multiplier? Product? What are the Multiplicand and the Multiplier called? 55. What is the sign of Multiplication? 56. What must the multiplier always be? What is the nature of the product? Explain. 57. Repeat the Multiplication Table. 61. Give the rule for Multiplication. 62. How do we prove Multiplication? 63. How is a number multiplied by 10? By 100? By 1 with any number of ciphers annexed? Why?

DIVISION.

65. 1. How many oranges, at 4 cents each, can be bought for 12 cents?

Solution.

As many oranges as there are times 4 cents in 12 cents; 4 cents are contained in 12 cents, 3 times; hence, 3 oranges, at 4 cents each, can be bought for 12 cents.

2. If I buy 5 apples for 10 cents, how much do I pay for each?

66. Division is the process of finding how many times one number is contained in another, or of finding one of the equal parts of a number.

67. The Dividend is the number to be divided.

The Divisor is the number by which to divide.

The Quotient is the number of times the dividend contains the divisor.

If the dividend does not contain the divisor an exact number of times, the part of the dividend which is left is called the Remainder.

68. The sign of division,÷, indicates that the number before it is to be divided by the number after it; or division may be indicated by writing the divisor under the dividend, with a line between the dividend and the divisor; thus, 8÷2 ==4, that is, 8 divided by 2 equals 4, or 2 in 8, 4 times.

3. How many are 6 ÷ 2?

Ans. 2 in 6, 3 times.

69. Of the divisor and quotient one must always be an

abstract number, while the other is of the same kind as the dividend.

Thus, in Ex. 1, 4 cents is contained in 12 cents, 3 times, not 3 oranges times. The divisor and dividend are of the same kind, and the quotient abstract.

In Ex. 2 we divide 10 cents into 5 equal parts of which one part is 2 cents; we do not divide 10 cents by 5 apples. The dividend and quotient are of the same kind, and the divisor abstract.

70. Oral Exercises.

4. 32 are how many times 4? 8? 2? 16?

5. 48 are how many times 4? 6 12 8 3 16?

6. 36 are how many times 12? 6? 9? 3? 4? 2?

7. 40 are how many times 8? 4? 2? 10? 5? 20?
8. 72 are how many times 2? 3? 4? 6? 8? 9? 12?

9. How many are 24÷6, or 24 ? 10. How many are 488, or 48? 11. How many are 6611, or ff? 12. How many are 8412, or 4? 13. How many are 63 ÷ 9, or 63? 14. How many are 486, or 48? 15. How many are 77 ÷ 11, or 17? 16. How many are 728, or 72 ? 17. How many are 96÷ 12, or £§? 18. How many are 888, or 88 ?

19. How many are 7212, or 72?

20. How many meters of broadcloth, at $3 a meter, can be bought for $69 ?

21. How many kilometers do I walk in one day, if I walk 55 kilometers in 11 days?

22. If 1 man can build a certain wall in 48 days, how long will it take 4 men?

In this example is the divisor abstract or concrete ?

23. If you buy 12 pounds of sugar for 96 cents, how much do you pay a pound?

71. Exercises for Written Work.

24. Divide 1384 by 4.

OPERATION.

Divisor, 4) 1384 Dividend.
Quotient, 346

Having written the divisor and dividend as in the margin, as 4 is not contained in the 1 that stands in thousands' place,

we say 4 in 13 hundreds, 3 hundreds times and 1 hundred remainder ; writing the 3 in hundreds' place in the quotient, we reduce the 1 hundred remainder to tens, that is, call it 10 tens, and adding it to the 8 tens, we have 18 tens; 4 in 18 tens, 4 tens times and 2 tens remainder; writing the 4 in tens' place in the quotient, we reduce the 2 tens remainder to units, that is, call it 20 units, and adding it to the 4 units we have 24 units; 24 units divided by 4 gives 6 units, which we write in units' place in the quotient, thus completing the division. Division with Decimals in the Dividend.

25. Divide 872.37 by 9.

OPERATION.

9) 872.37

Ans. 96.93

Proceeding exactly as in Ex. 24, at units we have 8 units remainder, which is equal to 80 tenths; 80 tenths and 3 tenths 83 tenths; 83 tenths divided by 9 give 9 tenths and 2 tenths remainder; 2 tenths 20 hundredths; 20 hundredths and 7 hundredths=27 hundredths; 27 hundredths divided by 9 give 3 hundredths; place the decimal point between units and tenths, and the division is complete.

=

This operation is called Short Division, and is usually adopted when the divisor is so small that the process may be readily carried in the mind. Hence,

72. To perform Short Division:

Rule.

Write the divisor at the left of the dividend, and draw a line between divisor and dividend, and a line under the dividend.

Divide the least number of figures at the left of the dividend that will contain the divisor, by the divisor, and write the quotient under the right-hand figure taken in the dividend; if anything remains, prefix it mentally to the next figure in the dividend, and divide the number thus formed as before, and so proceed till all the figures of the dividend have been employed. Place the decimal point between units and tenths.

NOTE. It is best, as soon as the units' figure of the quotient is written, to write the decimal point after it.

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