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WRITTEN EXERCISES. 1. Reduce yooo of a ton to the fraction of a pound.

ANALYSIS. - In this example Taboo x 20 x 100 = lb. we multiply, as in reduction

descending, by the numbers re

quired to reduce tons to pounds, applying the rule for the multiplication of common fractions.

2. Reduce .0002 T. to the decimal of a pound. .0002

ANALYSIS.—We multiply by the same num

bers in this as in the preceding example, .0040

applying the rule for the multiplication of 100 decimals. .4000 lb.

RULE. Multiply the given fraction, as in reduction of denominate numbers, by the numbers required to reduce it to the proper denomination.

3. Reduce ajo of a pound to the fraction of a penny. 4. .015 bu. is what decimal of a pint? 5. What fraction of a pint is of a gallon ? 6. Reduce 1. sq. rd. to the fraction of a sq. ft. 1. Reduce .0005 hr. to the decimal of a second. 8. 't of a rod is what fraction of an inch? 9. 25700 is what fraction of a grain? 10. What decimal of a sq. ft. is .035 sq.yd.? 11. Reduce or of a degree to the fraction of a second. 12. What decimal of a cubic foot is also of a cord?

13. Change 67 doo of a pound Troy to the decimal of a grain.

14. Change zoitoo of a ton to the fraction of an ounce. 15. Reduce 6250 of a leap year to the fraction of an hour. CASE II. To reduce a denominate fraction to an equivalent

fraction of a higher denomination.

ORAL EXERCISES. 1. What part of a foot is of an inch ? ANALYSIS.—One inch is by of a foot, and of an inch is of 12= z of a foot; or • 12= zo of a foot.

2. What part of a foot is .6 of an inch? ANALYSIS.—.6 -- 12=.05 of a foot.

3. What fraction of a pound is of a shilling? 4. What decimal of a gallon is .24 qt. ? 5. What fraction of a week is 7 of a day? 6. of a foot is what fraction of a yard? 7. % of a dime is what fraction of a dollar? 8. .9 of a dime is what decimal of a dollar? 9. Half a peck of oats is what fraction of a bushel ? 10. What.fraction of an eagle is a quarter of a dollar?

WRITTEN EXERCISES. 1. f of a lb. is what fraction of a ton?

*+14% = 20 = $ x Tho xt = 5000 T. ANALYSIS.— In this example we divide, as in reduction ascending, by the numbers required to reduce pounds to tons, applying the rule for the division of common fractions.

%. .4 of a lb. is what decimal of a ton? 1100).4000

ANALYSIS. - We divide by the same

numbers in this as in the preceding ex20).0040

ample, applying the rule for the division .0002 tons. of decimals.

RULE. Divide the given fraction, as in reduction of denominate numbers, by the numbers required to reduce it to the proper denomination.

3. 1 of a penny is what fraction of a pound? 4. Reduce .5 of a pint to the decimal of a gallon. 5. Reduce 4 of an inch to the fraction of a rod. 6. Reduce 36 half inches to the fraction of a yard. 7. .480 of a sq. rod is what decimal of an acre? 8. 2700 of a second is what fraction of an hour? 9. to of a cent is what part of an eagle? 10. What part of an eagle is .1 of a cent?

CASE III. To find the value of a denominate fraction in whole

numbers of a lower denomination.

ORAL EXERCISES. 1. Reduce 1 of a bushel to pecks. ANALYSIS.—In one bushel there are 4 pecks, and in 1 of a bushel there are 4 of 4 pecks = 2 pecks.

2. Reduce .5 of a bushel to pecks. ANALYSIS.—.5 X 4= 2.0 pecks.

3. How many inches in of a yard?
4. How many cents in of a dollar?
5. In .8 of a dollar there are how many cents ?
6. How many seconds in of a minute?
7. In .01 of a cwt. there are how many pounds?
8. Reduce of a pound to shillings.

9. How many glasses, each containing 3 gills, can be filled from of a gallon of water?

WRITTEN EXERCISES.
1. Reduce g of a gallon to quarts and pints.

ANALYSIS.—We reduce gallons

to quarts by multiplying by 4. š x 4= 12 = 11 qt.

Š x 4=1,2 qt. =14qt. We then 1 X 2= f = 1 pt.

reduce the įqt. to pints, by multiAns. 1 qt. 1 pt.

plying by 2. 1x 2=1 pint; and

the entire result is 1 qt. 1 pt. 2. Reduce .375 of a gallon to quarts and pints. .375

ANALYSIS.—We multiply the gallons by 4, as

in the preceding operation. .375 X 4=1.500 qt. 11.500

We then reduce the .500 qt. to pints, by multi

plying by 2. .500 X 2=1.000 pt.; and the entire 1.000 result is 1 qt. 1 pt. Ans. 1 qt. 1 pt.

RULE. Multiply the given fraction by the number required to reduce it to the next lower denomination. When the product is greater than a unit, change to a whole or mixed number, multiply the fractional part, if any, by the number required to reduce it to the next lower denomination, and proceed as before, until the reduction is completed.

3. Reduce o of a ton to pounds and ounces.

4. What is the value of of a rod in yards, feet, and inches?

5. Reduce .8534 bu. to pecks, quarts, and pints.

6. Add 4 of a day and 4 of an hour, and give the result in hours, minutes, and seconds.

7. From £.3805 subtract .3805 s., giving the result in shillings, pence, and farthings.

8. Three farms contain respectively 120g A., 1604 A., and 18516 A.; how many acres and square rods are there in all?

9. If I buy 124 cwt. of flour from one man, 16.25 cwt. from another, and 182 cwt. from a third, and then sell 19.75 cwt., how many cwt. and lb. do I have left?

10. Find the sum of of a day, i of an hour, á of an hour, and 1of a minute.

11. From g of an oz. of gold I sold { of a pwt.; how much had I remaining?

12. Find the sum of 18.546", 15.314°, and 1.099, in degrees, minutes, and seconds.

13. Reduce 128 pints to the fraction of a bushel, add { of a bushel to the result, and give the answer in bushels.

14. Reduce { of a bushel to the fraction of a pint, add 26 pt., and change the result to bushels.

CASE IV. To reduce one denominate number to the fractional

part of another.

ORAL EXERCISES. 1. What fraction of an hour is 15 minutes ? ANALYSIS.—In one hour there are 60 minutes, and 15 minutes =lhor of an hour.

2. What decimal of an hour is 15 minutes ? ANALYSIS.–15 minutes=1 of an hour. 1 of an hour=.25 of an hour.

3. What fraction of a gallon is 3 quarts? What decimal of a gallon?

4. Reduce 50 cents to the decimal of a dollar.

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