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SECTION XII. Parts of one are called fractions. Fractions may de expressed by figures, as well as whole numbers. It requires two numbers to express a fraction; one to show into how many parts one is divided, aná the other to show how many of those parts are used. For example, if we wish to express one half, (which means that one is divided into two equal arts, and that one part is used,) we must use the figure 2 to express that one is divided into two equal parts, and the figure 1 to show that one part is used. And these must be written in such a manher that we may always know what tach of them is intended to express.
One half is usually written thus, t; one numbe: above a line, and the other below it. The number below the line shows into how many parts one is divided, and the number above the line show's how inany parts are used.
One third is written Two thirds One fourth Three fourths Two fifths Example. 4 of an apple signifies that the apple is to be cut into 7 equal parts, and that 3 parts are to be used.
Let us apply an example to Plate II. $ refers to a square divided into 8 parts, and signifies that 5 parts are to be used.
We may observe, that, when one is divided into 3 parts, the parts are called thirds; when one is divided into 4 parts, the parts are called fourths, & that is, the fraction takes its name from the number of pants into whicli wae is divided. The number
under the line is called the denominator, because st gives name to the fraction; and the number above the line is called the numerator, because it shows the number of parts used. Thus it, 10 is the denominator and 3 the numerator.
N. B. The pupil must be made familiar with this mode of expressing fractions, and must be able to apply it to any familiar objects, as apples, oran ges, &c., and to the table, before he is allowed to proceed any farther. Particular care must be taken to make him understand what the denominator signifies, and what the numerator, as explained above. The denominator should always be explained first.
The following examples are a recapitulation of sume of the foregoing sections, for the purpose of showing the application of the above method of writing fractions.
See Section VIII, A.
A. 1. In 2 how many times ]? Ans. 2. In 3 how many times ? Ans. . 3. In 2 how many times ? Ans. * 4. Iz 4 how many times $? 5. In 6 how many times 1 6. In 7 how many times 7. In 8 how many times $ 8. In 27t how many times ? 9. In 37 how many times ? 10. Reduce 41 to an improper fraction. I 11. Reduce 37 to an improper
fraction." 12. Reduce 5} to an improper fraction.
* When the namerator is larger than the denominator, tlae fuaeton is called an improper fraction. + 2 is read two and 1 half. It is ealled a mixed number
That is to find low many fifths there are in four wow! Gifts.
13. Reduce og to an improper fraction. 14. Reduce 837 to an improper fraction. .5. Reduce 94 to an improper fraction,
B. 1. are how many times 1 ? 2. are how many times 1 ? 3. Z are how many times 1 ? 4. I are how many times 1 ? 5. f are how many times 1 ? 8. V are how many times 1 ? 7. V are how many times 1 : 8. * are how many times 1? 9. Yo are how many times 17 10. 47 are how many times 1 ?
See Section IX.
A. 1. How much is 3 times? 2. How much is 4 times ? 3. How much is 3 times ? 4. How much is 4 times? 5. How much is 6 times 6. How much is 6 times ? 7. How much is 8 times to? 8. How much is 9 times ? 9. How much is 10 times 10. How much is 9 times
B. 1. How much is 3 times ?
4. !2 is of what number? 5. 15 is of what number? 6. 18 is of what number? 7. 20 is f of what number? 8. 24 18 of what number? 9. 28 is of what number? 10. 30 is to of what number? 11. 3 is of what number? 12. 4 is & of what number? 13. 5 is of what number? 14. 8 is of what number? 15. 9 is of what number? 16. 17 is of what number? 17. 25 is of what number? 18. 38 is of what number? 19. 43 is in of what number? 20. 54 is yo of what number?
Miscellaneous Examples. 1. A man sold 8 yards of cloth for 3f dollars yard; what did it come to?
2. A man sold a horse for 76 dollars, which was of what it cost him; how much did it cost him ?
3. A man sold off of a gallon of wine for 40 cents; what was that a gallon ?
4. If it will take 17 yards of cloth to make a cost, how many vards will it take to make 7 coats ?
5. If i horse consume 37 bushels of oats in days, how much would 2 horses in 5 days ?
6.' If, when the days are 91 hours long, a man perform a journey in 10 days, in how many days would he perform it when the days are 12 hours long?
7. A man sold 8 yards of cloth for 7 dollars yard, and received 8 firkins of butter at of dollars a firkin, how much was then due to him?
& Two man are 38 miles apart, and are traves