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2. Sound moves about 1142 feet per second. How many feet will it move in 144 seconds?

By the question, we know that in one second sound travels 1142 feet; therefore, in 144 seconds it travels 144 x 1142 feet.

Multiplication.

Factors{144 multiplier

1142 multiplicand

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Proof.

144

1142

288

576

144

144

164448

3. In a plantation there are 274 rows of trees, each containing 485 trees. How many trees are there in the plantation? 4. How many times does the hammer of a clock strike in 365 days, or one year, at 156 strokes per day?

5. One mile contains 1760 yards. How many yards are there from the earth to the moon, the distance being 240000 miles? 6. Perform the following multiplications :—24 × 762; 63×196; 5704×487; 7800 × 365; 3600 × 49200.

7. How many hours are there in 365 days, of 24 hours each? 8. The equator, like every other circumference, is supposed to be divided into 360 parts, or degrees, each containing 69 miles. How many miles is it round the earth?

9. Light travels with a velocity of 192000 miles per second, and the sun's light reaches us in 8 minutes 13 seconds, or in 493 seconds. What is our distance from the sun?

10. Two persons start at the same time, one from London and the other from Worksop; the first travels 18 miles per day, and the other 19 miles; they meet after travelling four days. How far are the two places from each other?

11. A person owns 79 horses, worth £26 each, on an average; and 347 head of cattle, valued at £13 each. What is the value of all?

12. A draper bought 347 yards of cloth, at 27 shillings per yard, and 276 yards at 18 shillings, for which he paid 12337 shillings. How much has he yet to pay?

13. Reckoning every year of 365 days 6 hours, how is it since the birth of our Lord, which took place ago?

many hours 1853 years

14. A boy who is 14 years 8 months and 14 days old, wishes to know how many seconds he has lived; three years of his life were leap years; of the 8 months, 5 were of 31 days, 2 of 30 days, and the last of 28 days.

15. A wheel of a locomotive engine makes 25 revolutions in one second. How many revolutions will it make in 7 hours 17 minutes and 24 seconds? Also, how many yards has it run over, the wheel being six yards round?

16. A merchant employs 12 clerks, three at the rate of £240 annually, five at the rate of £180, and four at £80; 14 servants, eight of them at £22 each, on the average, and the six others at £15 each; for house rent, &c., he spends £1400; the house-keeping expenses amount to £2200. In one year he did business to the amount of £224600, upon which he laid out £206700. What were his profits at the year's end?

DIVISION.

77. If eight apples are to be parted, or divided equally between two persons, how many will each receive?

In this question it is proposed to make as many equal shares, or portions of the apples, as there are persons, or to divide 8 by 2, or to see how many times 2 is contained in 8, and the answer is 4.

Other questions similar to this might be proposed by the teacher, and solved mentally.

78. Therefore, division consists in dividing numbers into equal parts, or in finding how many times one number is contained in another.

79. The number which is divided is called the dividend, the number we divide by, the divisor, and the number resulting from the operation is named the quotient.

In the previous question, which number is the dividend, which the divisor, and which the quotient?

8, divided by 2, equal 4, is expressed thus: 8÷2, or

8

2=4.

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64 60

There are various methods of solution, for instance,=

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64

= 10+6=16.

&c. But the best method of solution is this:

4 is contained in 6 tens, 1 tens, and 2 tens added to the 4 units, 2 tens+4 units=24 units. in 24 units 6 units times.

Divide 16422 by 6.

4

over, which are

4 is contained

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Solution 6 is contained in 16 thousands 2 thousand times, and 4 thousands over, 4 thousands +4 hundreds = 44 hundreds; 6 is contained in 44 hundreds 7 hundred times, and 2 hundreds over, 2 hundreds+2 tens=22 tens; 6 is contained in 22 tens 3 tens, and 4 over, 4 tens+2 units=42 units; 6 is contained in 42 units 7 times; therefore, the quotient is 2737.

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84. The process is rather longer when the divisor is larger than 12. Example: Divide 6164 by 46.

46)6164(134

46

156

138

184

184

The divisor is placed to the left of the dividend, separated by a small curved line; on the right, draw another line. Take the least number of figures on the left of the dividend, that will contain the divisor, find how many times they contain it, and place the result on the right as the first figure of the quotient; and the product arising from the multiplication of the divisor by this figure being subtracted from the dividend, annex to the remainder the next figure of the dividend, and divide the result as before; and proceed thus till all the figures of the dividend have been brought down or used.

If, after having annexed a figure to the remainder, the divisor is not contained in it, we place zero in the quotient, annex the

next figure of the dividend to the remainder, and proceed as before.

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86. It very often occurs that the divisor is not contained exactly in the dividend, then the last remainder may be joined to the quotient, under this form: +remainder...... (or see § 92).

87. Since the quotient is the number of times the divisor is contained in the dividend, it follows that the quotient multiplied by the divisor must necessarily be equal to the dividend, minus the remainder, if there be any. This affords a method of ascertaining whether a divisor has been correctly performed.

88. EXERCISES.

1. The annual income of a person is £38360. How much is that per day?

The income must be divided into 365 equal parts, and one of them is the daily income; therefore, £38360 must be divided by 365.

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2. 648 chests of tea cost £7128. What is the price of one chest?

3. What number is 25 times less than 3675 ?

4. £8400 are to be divided equally amongst six persons. How much would each individual's share be?

5. The dividend is 156970, and the divisor 2854. Find the quotient.

6. The dividend is 8760, and the quotient 24. Find the divisor. 7. What number, multiplied by 54, gives 9990 as product?

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