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5. Divide 1 by f1.
6. Divide 9 by of .
7. How many times is

8. How many times is

A. 37%.

A. 37.

contained in ?

Ꭿ. 17.

contained in 1? A. 215. 9. What number multiplied by will make? A. 21.

REDUCTION OF FRACTIONS.

It will be recollected, that in Reduction (¶ XXIX.) whole numbers were brought from higher to lower denominations by multiplication, and from lower to higher denominations by division; hence, fractions of one denomination may be reduced to another after the same manner, and by the same rules.

¶ XLVIII. TO REDUCE WHOLE NUMBERS TO THE FRACTION OF A GREATER DENOMINATION.

1. What part of 2 miles is 1 mile ?

2. What part of 4 miles is 1 mile? Is 2 miles? Is 3 miles? 3. What part of 1 yd. is 1 qr.? Is 2 qrs.? Is 3 qrs.? 4. What part of 8 gallons is 1 gallon? Is 3 gallons? 5. What part of 9 oz. is 1 oz.? Is 2 oz.? Is 5 oz.? 6. What part of 7 yds. is 1 yd.? Is 6 yds.? Is 7 yds.? 7. What part of $21 is $17? Is $11? Is $13? 8. What part of 271 inches is 11 in. ? Is 251 in.? 9. What part of 1 month is 1 day? Is 2 days? 10. What part of 1 hour is 11 minutes? Is 21 minutes? 11. What part of 19 cents is 11 cents? Is 3 cents? 12. What part of 1 d. is 1 farthing? Is 2 13. What part of 1 s. is 1 d.? Is 2 d.?

1. What part of a bushel is 3 pks. 4 qts.?

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qrs.? Is 3 qrs.? Îs 3 d.?

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From these illustrations we derive the following

RULE.

Q. How do you obtain the numerator?

A. Bring the given denominations to the lowest denomination mentioned, for a numerator.

Q. How do you obtain the denominator?

A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator.

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3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz.?

A. 788.

4. What part of 1 yard is 3 qrs. 3 na.?
5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt.?

A. 18.

6. What part of 1 tun is 1 gallon, 0 qts. 2 pts.

7. What part of 15 pipes is 25 galls.?
8. What part of 2 miles is 7 fur. 11 in. 2 b. c.?

9. What part of 1 month is 19 days? 10. What part of 1 month is 25 days, 13 hours?

A. 82. 1 gill? 1.8764. A. 375.

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11. What part of 1 month is 22 days, 15 h. 1 min.?

TXLIX.

A. $18.

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TO REDUCE A FRACTION TO WHOLE NUM

BERS OF LESS DENOMINATIONS, OR, TO FIND THE VALUE OF A FRACTION.

of a lb.?

of a lb.?

1. How much is of a shilling? How much of a lb.? of a lb.? of a lb.? 1 z's of 1 qr. of a cwt.??? 28?? 18? 27? an hour?? ??

Operation by Slate illustrated.

1. What is the value of of a pound?

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Q. What do you multiply the numerator by?

A. By as many of the next denomination as make one of that; that is, pounds by what makes a pound, ounces by what makes an ounce, as in Reduction of whole numbers.

Q. What do you divide the product by?
A. By the denominator.

Q. If there be a remainder, how do you proceed?
A. Multiply and divide as before.

More Exercises for the Slate.

2. What is the value of

3. What is the value of 4. What is the value of

Dwts. 161.

of a cwt.? A. 3 qrs.

of an acre? A. 1 rood, 134rds. 2% of a pound Troy? A. 10 oz. 8

5. What is the value of of a hogshead? 1292 qts.

A. 49 gallons

6. What is the value of of a pound avoirdupois? A. 1lb. 1437 oz.

7. What is the value of

9

90 of a hogshead? A. 50 gallons.

13

8. What is the value of of a day? A. 16 hours, 36 min. 55 sec.

1 L. TO REDUCE FRACTIONS OF A HIGHER DENOMINA

TION INTO A LOWER.

We have seen (¶ XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators.

1. Reduce 40 £. to the fraction of a penny.

OPERATION.

Numer. 1

20 s.

20

12 d.

New numer. 240

Then, 240

In this example, we multi

ply the 1, in 40, as in Re-
duction of whole numbers,
viz., pounds by what makes a
pound, shillings by what
makes a shilling, &c. But
this operation may be express-
ed differently, thus ;
20 x 12-18=d.; or, by
dividing the denominators,

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20=24÷12=

Denom. 480

d., Ans., as before, in its lowest terms.

RULE.

Q. How, then, would you proceed?

A. Multiply the fraction, as in Reduction of whole numbers.

More Exercises for the Slate.

2. Reduce o of a pound to the fraction of a shilling.

A. 1 S.

3. Reduce 1920 of a pound to the fraction of a farthing.

A. gr.

4. Reduce Tobs of a hogshead to the fraction of a gallon.

A. 6 gal.

5. Reduce of a bushel to the fraction of a quart.

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6. Reduce TT of a day to the fraction of a minute.

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7. Reduce Tog of a cwt. to the fraction of a pound.

8. Reduce 9. Reduce

A. lb.

of a hhd. to the fraction of a pint. A. pt.

of a pound to the fraction of a shilling
A. }&

LI. TO REDUCE FRACTIONS OF A LOWER DENOMINATION INTO A HIGHER.

We have seen, that, to divide a fraction, (T XL.) we must multiply the denominator, or divide the numerator.

This rule is the reverse of the last, (T L.) and proves it. 1. Reduce of a penny to the fraction of a pound.

OPERATION.
Denom. 2

12

24

20

New denom. 480

Then, ʊ, Ans.

In this example, we divide as in Reduction, ( XXIX.) viz., pence by pence, shillings by shillings; but, in order for this, we must either multiply the denominator or divide the numerator by the same numbers that we should divide by in Reduction of whole numbers. The same result will be obtained if performed thus :

d.

8.

× 12×20=490 £., Ans.

Hence the following

Q. How do you proce

RULE.

A. Divide as in Reduction of whole numbers.

More Exercises for the Slate.

2. Reduce 1⁄2 of a shilling to the fraction of a pound.

A. zło £.

3. Reduce of a farthing to the fraction of a pound.

A. T20 £.

4. Reduce of a gallon to the fraction of a hogshead.

A. Too hhd.

5. Reduce of a quart to the fraction of a bushel.

A. TT bu.

6. Reduce of a minute to the fraction of a day.

A. TIT.

7. Reduce of a pound to the fraction of a hundred weight.

A. TO 8.

8. Reduce of a pint to the fraction of a hogshead.

A. 2520=630.

9. Reduce of a shilling to the fraction of a pound,

A..

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