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EXAMPLES.

1. In $16.50 how many pounds and shillings, in sterling, or English money; a dollar being four shillings and six pence, or 54 pence?

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£3 14s. 3d. Answer.

2. In 33 dollars, how many pounds, &c.?

Ans. £7. 88.-6d.

3. In 1000000 dollars, how many pounds sterling?

Ans. £225000.*

4. Reduce 432 dollars into the currency of Canada and Nova Scotia, a dollar being equal to five shillings; or 60 pence. Ans. £108. 5. In $490.50 how many pounds, shillings, &c. same currency? Ans. £122 12s. 6d. 6. Bring $150.25, into the currency of New England, Virginia, and Kentucky, a dollar, being equal to 72 pence. Ans. £45. 1s. 6d.

Questions.

1. What does Exchange teach?

2. How do you reduce the currency of any one of the United States to Federal Money?

3. Does this rule apply to the currency of any other country?

4. How do you change Federal Money into pounds, shillings, and pence of any state or country? 5. Among the various kinds of money, what kind is the most easily reckoned?

*Federal Money may, also, be changed into English Money, by multiplying the dollars by 9, and dividing the product by 40.

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In using the Fractional Plate, the student must count the white spaces, and not the black lines. The first row of squares, or white spaces, at the top, are whole numbers; the second row is divided into halves; the third, into thirds, and so on from the top to the bottom. Thus it may be shown, at one glance, that 7 halves make three and a half, or that 8 thirds make 2 and 2 thirds, &c.

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Fractions are broken numbers, expressing any assignable part of an unit, or whole number. They are represented by two numbers placed one above another, with a line drawn between them; thus, t, &c. signifying two fifths and five eights.

The figure above the line is called the numerator, and that below the line, the denominator. The denominator shows into how many equal parts the whole quantity is divided, and represents the divisor in division. The numerator shows how many of those parts are expressed by the fraction; being the remainder after division. Both these numbers are sometimes called the terms of the fraction.

Questions to prepare the learner for this Rule.

1. If a pear be cut in two equal parts, what is one of those parts called?

Ans, a half.

2. If you cut a pear into three equal parts, what is one of those parts called? Ans, one third.

3. How many thirds of a thing make the whole? 4. If a pear be cut into four equal parts, what is one of those parts called? Ans. one fourth. What are two of the parts called? Ans. two fourths. What are three of them called?

Ans. three fourths.

5. How many fourths of a thing make the whole? 6. If an orange be cut into five equal parts, what is one of the parts called? Ans. one fifth. What are two of the parts called? Ans. two fifths. What are three of them called? Ans. three fifths. What are four of them called? Ans. four fifths. 7. How many fifths of a thing make the whole? 8. If you cut a pear into six equal parts, what is one of the parts called? What are two of them called?— What are three of them called? What are four of them called?

9. How many thirds are there in one? How many fourths? If four fourths make the whole, what part are two fourths? What part of three is one? What part of four are two? What part of six are two?

What part of eight are
What part of 10 are 2?

What part of eight are two? six? What part of 9 are 6? What part of 10 are 4? What part of 10 are 7? What part of 12 are 6? What part of 12 are 4? What part of 12 are 3? What part of 12 are 2?

10. How many are two fourths of 12? How many are three fourths of 12? Two thirds of 12, are how many? How many are 5 times 8? In one eighth of 40, how many? In three eights of 40, how many? Four eights of 40, are how many? Then of any rimber, or of any thing, amount to how many, or how much? How many are of 30? How many are of 30? How many in of 60? In of 60, how many In of 60, how many In of 60, how many? How } many are of 60? How many are of 60? How many are of 60 In 2 and 3, how many fifths? In 5 and how many fifths? In of 100, how many? In 4 of 100 cents, or 1 dollar, how much? How much are and ? How much are and 4? How much are and? How much are How much are and 4? How much are 2, 3, and Iny, how many? In 3, how many? If you take from one dollar, how much will remain? If you take from one dollar, how much will remain? If you take from a pound, how much will remain? If you take from one, how much will remain? How many fourths are 2 times ? How many are 5 times? How many are 3 times ? In 11, how many? In 18, how many?

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11. If one half, three fourths and a quarter, be added, how much will be their amount?

12. If you take two eights from eleven eights, how much will remain?

13. What is a proper fraction?

Ans. When the numerator is less than the denominator, as, or 3, &c.

14. What is an improper fraction?

Ans. It is that in which the numerator is equal, or superior to the denominator; as, f, or §, or 7, &c. 15. What is a simple fraction?

Ans. It is a fraction expressed in a as, t, 4, §.

simple form;

16. What is a compound fraction?

Ans. It is the fraction of a fraction, or several fractions connected together with the word of between them; as, of of; or of 7, &c. which are read thus, one half of two thirds; &c.

17. What is a mixed number?

Ans. It is composed of a whole number and a fraction; as 34, or 121.

18. What is the common measure of two or more numbers?

Ans. It is that number which will divide each of them without a remainder; thus 5 is the common measure of 10, 20, and 30; and the greatest number that will do this, is called the greatest common measure.

19. What is meant by the common multiple?

Ans. Any number which can be measured by two or more numbers, is called the common multiple of those numbers; and if it be the least number that can be so measured, it is called the least common multiple; thus 40, 60, 80, 100; are multiples of 4 and 5; but their least common multiple is 20.

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20. When is a fraction said to be in its lowest terms? Ans. When it is expressed by the smallest numbers possible.

21. What is meant by a prime number?

Ans. It is a number which can only be measured by itself, or an unit.

22. What is meant by a composite number?

Ans. That number, which is produced by multiplying several numbers together, is called a composite number.

23. What is a perfect number?

Ans. A perfect number is one that is equal to the sum of its aliquot parts.*

*The following perfect numbers are all which are, at present known.

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