8. If sound moves 1142 feet in a second, how far will it move in one minute? Ans. 68520 feet.

ART. 43. When the multiplier is 1 with one or more ciphers annexed to it, as 10, 100, &c.

Ex. 1. In 1 day there are 24 hours; how many hours in 10 days? In 100 days?

OPERATION.

Multiplicand 24 24
Multiplier

Product

10 100

240 2400 Or thus, 240, 2400.

Answers. 240, 2400.

The removal of a figure one place to the left makes the value expressed tenfold. (Art. 7.) Therefore, by annexing one cipher to 24, the multiplicand, each figure is removed one place to the left, and the value expressed made tenfold, or multiplied by 10; and by annexing two ciphers, each figure is removed two places to the left, and the value expressed made one hundredfold, or multiplied by 100. Hence the following

RULE. - Annex to the multiplicand as many ciphers as has the multiplier. The number thus formed will be the product required.

ART. 44. When there are ciphers on the right hand of the multiplier or multiplicand, or both.

Ex. 1. What will 600 acres of land cost at 20 dollars per Ans 12,000 dollars.

acre?

OPERATION.

Multiplicand 600
Multiplier 20

Product 12000

The multiplicand may be resolved into the factors 6 and 100, and the multiplier into the factors 2 and 10. Now, it is evident (Art. 42), if these several factors be multiplied together, they will produce the same product as the original factors 600 and 20. Thus 6 X 2 = 12, and 12 × 100=1200, and 1200 × 10=12000, the same result as in the operation. Hence the following

QUESTIONS. Art. 43. What is the effect of removing a figure one place to the left? What is the effect of annexing a cipher to any figure or number? Two ciphers? &c. What is the rule when the multiplier is 1 with ciphers annexed? Art 44. How do you arrange the figures for multiplication, when there are ciphers on the right hand of either the multiplier or multiplicand, or both? Why does multiplying the significant figures and annexing the ciphers produce the true product?

RULE.

Write the significant figures of the multiplier under those of the multiplicand, and multiply them together. To their product annex as many ciphers as there are on the right of both multiplicand and multiplier.

8. Multiply twenty-nine millions two thousand nine hundred and nine by four hundred and four thousand.

Ans. 11717175236000.

9. Multiply eighty-seven millions by eight hundred thousand seven hundred. Ans. 69660900000000. 10. Multiply one million one thousand one hundred by nine hundred nine thousand and ninety. Ans. 910089999000. 11. Multiply forty-nine millions and forty-nine by four hundred and ninety thousand. Ans 24010024010000.

12. Multiply two hundred millions two hundred by two millions two thousand and two. Ans. 400400800400400. 13. Multiply four millions forty thousand four hundred by three hundred three thousand. Ans. 1224241200000. 14. Multiply three hundred thousand thirty by forty-seven thousand seventy. Ans. 14122412100. 15. Multiply fifteen millions one hundred by two thousand two hundred. Ans. 33000220000.

16. Multiply one billion twenty thousand by one thousand Ans. 1100022000000.

one hundred.

ART. 45.

§ V. DIVISION.

MENTAL EXERCISES.

WHEN it is required to find how many times one number contains another, the process is called Division.

Ex. 1. A boy has 32 cents, which he wishes to give to 8 of his companions, to each an equal number; how many must each receive?

ILLUSTRATION.

-It is evident that each boy must receive as many cents as the number 8 is contained times in 32. We therefore inquire what number 8 must be multiplied by to make 32. By trial, we find that 4 is the number; because 4 times 8 make 32. Hence 8 is contained in 32 4 times, and the boys receive 4 cents apiece.

The following table should be studied by the learner to aid him in solving questions in division:

2. A farmer received 8 dollars for 2 sheep; what was the price of each ?

ILLUSTRATION.

It is evident, since he received 8 dollars for 2 sheep, for 1 sheep he must receive as many dollars as 2 is contained times in 8. 2 is contained in 8 4 times, because 4 times 2 are 8; hence 4 dollars was the price of each sheep.

3. A man gave 15 dollars for 3 barrels of flour; what was the cost of each barrel ?

4. A lady divided 20 oranges among her 5 daughters; how many did each receive?

5. If 4 casks of lime cost 12 dollars, what costs 1 cask?

6. A laborer earned 48 shillings in 6 days; what did he receive per day?

7. A man can perform a certain piece of labor in 30 days; how long will it take five men to do the same?

8. When 72 dollars are paid for 8 acres of land, what costs 1 acre? What cost 3 acres?

9. If 21 pounds of flour can be obtained for 3 dollars, how inuch can be obtained for 1 dollar? How much for 8 dollars? How much for 9 dollars?

10. Gave 56 cents for 8 pounds of raisins; what costs 1 pound? What cost 7 pounds?

11. If a man walk 24 miles in 6 hours, how far will he walk in 1 hour? How far in 10 hours?

12. Paid 56 dollars for 7 hundred weight of sugar; what costs 1 hundred weight? What cost 10 hundred weight?

13. If 5 horses will eat a load of hay in 1 week, how long would it last 1 horse?

How many times 4? How 10?

How many times 4? How

14. In 20, how many times 2? many times 5? How many times 15. In 24, how many times 3? many times 6? How many times 8? 16. How many times 7 in 21? In 28? In 14? In 63? In 77? In 70?

In 56? In 35?

In 84?

ART. 46. The pupil will now perceive that

DIVISION is the process of finding how many times one number is contained in another.

In division there are three principal terms: the Dividend the Divisor, and the Quotient, or answer.

The dividend is the number to be divided.

The divisor is the number by which we divide.

The quotient is the number of times the divisor is contained in the dividend.

NOTE. Quotient is derived from the Latin word quoties, which signi fies how often, or how many times.

When the dividend does not contain the divisor an exact number of times, the excess is called a remainder, and may be regarded as a fourth term in the division. The remainder, being part of the dividend, will always be of the same denomination or kind as the dividend, and must always be less than the divisor.

ART. 47. SIGNS. The sign of division is a short horizontal line, with a dot above it and another below; thus, . It shows that the number before it is to be divided by the number after it. The expression 6 ÷ 2 = 3 is read, 6 divided by 2 is equal to 3.

Division is also indicated by writing the dividend above a short horizontal line and the divisor below; thus, g. The expression = 3 is read, 6 divided by 2 is equal to 3.

There is a third method of indicating division, by a curved line placed between the divisor and dividend. Thus, the expression 6) 12 shows that 12 is to be divided by 6.

EXERCISES FOR THE SLATE.

ART. 48. The method of operation by Short Division, or when the divisor does not exceed 12.

Ex. 1. Divide 8574 dollars equally among 6 men.

Ans. 1429 dollars.

QUESTIONS. Art. 46. What is division? What are the three principal terms in division? What is the dividend? What is the divisor? What is the quotient? What the remainder? What will be the denomination of the remainder? How does it compare with the divisor? - Art. 47. What is the first sign of division, and what does it show? What is the second, and what does it show? What is the third, and what does it show? - Art. 48. What is short division?