SUPPLEMENT

TO THE FOUR FUNDAMENTAL RULES OF ARITHMETIC, VIZ:

ADDITION, SUBTRACTION, MULTIPLICATION, AND

DIVISION.

EXERCISES.

1. A man purchased a farm for 6720 dollars; sold it for 199 dollars more than he gave. For how much did he sell it? Ans. 6919 dollars.

2. Suppose a tree broken by the wind 39 feet from the ground, and the part broken off to be 56 feet in length. How high was the tree? Ans. 95 feet.

3. A merchant having 784 bushels of salt, sold 99 bushels. How many had he left? Ans. 685 bushels.

4. A man left his estate, valued at 8956 dollars, to his wife and daughters, giving his wife 4688 dollars. How much did the daughters receive?

Ans. 4268 dollars.

5. Sir Isaac Newton was born in the year 1642, and died in the year 1727. What was his age? Ans. 85 years.

6. The greater of two numbers is 624; their difference is 89. What is the less number? Ans. 535.

7. What will 58 yards of broadcloth cost, at 4 dollars per yard? Ans. 232 dollars. 8. Bought 122 bushels of wheat, at 2 dollars a bushel; 8 oxen for 27 dollars each; 4 cows, 16 dollars each, and a wagon for 60 dollars. How much was paid for the whole, and how much more for the wheat and oxen than for the cows and wagon?

Ans.

{

J 584.

336.

9. The factors of a certain number are the difference between 1632 and 1700, and between 94 and 5 dozen. What is that number? Ans. 2312.

10. How many barrels of flour may be bought for 6721 dollars, at 13 dollars per barrel? Ans. 517 barrels. 11. Paid 57600 cents for eggs, paying at the rate of 12 cents a dozen. How many dozen did I buy?

Ans. 4800 dozen.

12. What will 168 firkins of butter cost, at 29 dollars a firkin? Ans. 4872 dollars.

13. A man bought at vendue the following articles, viz. :— A colt for 18 dollars; a horse for four times as much as the colt; a wagon for 8 dollars less than the cost of the horse; 4 cows for 4 dollars more than the cost of the wagon; 12 sheep, at 3 dollars each; a plough for 5 dollars; a ton of hay for 16 dollars; and a pair of oxen for four times the cost of the hay. Now, supposing he sells the whole for 527 dollars, how much does he gain; and if with the gain he pays 4 men, to whom he is in debt, equal sums, what does each receive? Ans. 46 dollars.

14. How many square feet in a board 12 feet long, and 2 feet wide?

It is evident that a board 12 feet long and 1 foot wide would contain 12 square feet; then a board of the same length and 2 feet in width would contain twice as many feet. The answer, then, is 12 x2=24 feet.

15. How many feet in length is a board which contains 24 square feet, and is 2 feet in width ? Ans. 12 feet. It is evident that this question is the reverse of the prece

ding.

Then, 24-2=12.

16. How many square feet of boards in a log which will make 26 boards, 15 feet in length and 3 feet in width?

Ans. 1170.

17. How many square feet will it take for the floor of a hall, 40 feet long, 22 in width, allowing 24 feet for waste?

Ans. 856 feet. 18. What is the width of a house which is 42 feet long, and the length and width multiplied make 1260 feet?

Ans. 30 feet.

19. Supposing it take 60 yards of carpeting to cover the floor of a room 15 feet in width, what is the length of the room, and how much will be the cost of the carpeting, at 1 dollar 50 cents per yard? 12 yds. in length.

Ans. {

9000 cents.

20. How much money will a man lay up in a year of 52 weeks, if he lay up 25 cents a day, Sundays excepted?

Ans. 7800 cents.

21. What is the difference between 7 times 35, and 7 times 5 and 30?

Ans. 180.

22. How many days, months and years will a man be in travelling around the globe, it being 25000 miles, at the rate of 5 miles per hour, 10 hours in a day?

23. The less of two numbers is 432; the difference between them is 175. What is the greater? Ans. 607. 24. The remainder of a sum in Division is 423; the quotient 423; the divisor is the sum of both and 19 more. What, then, was the number to be divided? Ans. 366318.

25. What number, multiplied by 72084, will produce 5190048?

Ans. 72.

26. The remainder of a sum in Division is 244; the quotient 1269; the divisor is twice the sum of the remainder, less 32. What was the sum divided? Ans. 578908.

27. What is that number, which, being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 be subtracted, to the remainder 30 added, and half the sum shall make 35?

Ans. 700.

Art. 48.-Exercises in the use of the signs.

1. Write 9, plus 3, minus 7, plus 4.

9+3-7+4-9 Ans. 2. Write the sum of 9 plus 3, minus the sum of 7 plus 4. 9+3-7+4=1 Ans. 3. Write the sum of the products of 8 into 7, and 9 into 4. 8×79×4=92 Ans. 4. Write the product of the sum of 8 and 7 into the sum of 9 and 4. 8+7x9+4=195 Ans. 5. Write the difference of the products of 8 into 7, and 9 into 4. 8X7-9X4=20 Ans. 6. Write the product of the difference of 8 and 7, and 9 and 4.

8-7X9-4-5 Ans.

7. Write the sum of the difference of 9 and 3, and 7 and 4.

8. Write the product of 16 into 2, divided by 8.

16X2 8 4 Ans.

9. Write 16 divided by the product of 8 into 2.

16 8X2-1 Ans.

10. Write the quotient of 16 divided by 2, divided by 8. 16 2 8 1 Ans.

11. Write 16 divided by the quotient of 8 divided by 2. 16 8 2 4 Ans.

Art. 49. Let the scholar write and perform the following questions, as the preceding.

1. What is the product of the sum of 16 sum of 9 and 10?

2. What is the sum of the products of 7 into 8 ?

and 12 into the Ans. 532. into 11, and 5

Ans. 117.

3. What is the difference of the products of 9 into 12, and 7 into 9 ?

Ans. 45.

4. Divide the sum of 5 and 19, by the sum of 3 and 5.

Ans. 3. 5. Divide the product of 7 into 10, by the product of 5 into 7.

6. Divide the product of 8 into 16, by the sum of

Ans. 2.

9 and 7. Ans. 8.

7. Divide the sum of 15 and 17, by the product of 4 into 2.

RATIO, OR RELATION OF NUMBERS.

Ans. 4.

Art. 50.-The ratio, or relation of one number to another, is found by division. It is the quotient arising from dividing one number by another. Thus the ratio of 8 to 4 is 2; 8-4=2. The quotient shows that the dividend is twice as large as the divisor. Instead, therefore, of the word quotient, we might use the word ratio.

When the dividend is less than the divisor, the ratio is expressed by writing the divisor under the dividend.

Art. 51. Since no new principle is ever discovered or needed in arithmetical operations not embraced in the simple rules, it is important that the student should understand these

QUESTION.-1. What is ratio?

rules, in all their varied applications. New names, and a new mode of writing and solving questions, naturally suggest the idea of new principles. Hence the beginner, in Fractions, is generally perplexed; to avoid this, fractions are written, and the various operations are explained, in the following exercises, as in whole numbers.

Operation.

1. Divide 2 by 2. 2)2=1 Ans.

Operation.

The quotient of 2 divided by 2, is a unit, or 1.

2. Divide 1 by 2. 2)1=Ans. by 2, is something less than The quotient of 1 divided

a unit, and is called a fraction. A fraction is, therefore, the result of division. The terms of the division, which were dividend and divisor, are now the terms of the fraction, and assume the new names, "Numerator and Denominator." The scholar will, therefore, bear in mind, that numerator is the same as dividend, and denominator the same as divisor. The fraction, as a quotient, expresses the relation of dividend to divisor; that is, it shows that the dividend was half as large as the divisor. But it may still be regarded as division implied-the numerator may be considered as a whole number, and the expression read, 1 divided by 2.

3. Multiply, or 1 divided by 2, by 2.

Operation.

1 Ans.

It is evident that twice, or twice 1 divided by 2, is equal to unity, or 1. To multiply the dividend is the same as to divide the divisor. Twice 1 divided by 2, is multiplication and division of whole numbers, and requires no new rule.

4. Divide, or 1 divided by 2, by 2. Operation. 211

To obtain one half of any number, we divide it by 2. But our dividend is a number already divided; the operation, therefore, is a 4|1=Ans. repetition of division, and consequently no new rule is necessary.

5. Multiply by 3. That is, multiply 3 divided by 4, by 2 divided by 3.