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6. Diride 1 by it. A. 376. 6. Divide 94 by top A. 37. 7. How many times is $ contained in ? A. 1). 8. How many times is to contained in if? A. 2155. 9. What number multiplied by 4 will make 13? A. 218.

REDUCTION OF FRACTIONS. It will be recollected, that in Reduction (1 XXIX.) whole pumbers 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? Is2 miles? Is 3 miles? 3. What part of 1 yd. is 1 qr.? Is 2 qrs.? Is 3 grs.? 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 yde.? 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 $1 minutes ? 11. What part of 19 cents is 11 cents ? Is 3 cents ? 12. What part of 1 d. is 1 farthing? Is 2 qrs.? Is 3 qrs.? 13. What part of 1 s. is 1 d.? Iš 2 d.? Is 3 d.? 1. What part of a bushel is 3. pks. 4 qts.! OPERATION.

1 ba.=32 qts., and 3 pks 4 qts.

3 pks. 4 qts.=28 qls. 8

Then, as 32 qts. make

1 bushel, 1 qt. is 24

of a bushel, and 28 qis. 4

28 times 32 = 32 Denom. 28 Numer.

} bu. Ans., the same Then 33 = }, Ans.

1 bu.

as before.

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 de nomination into the same denomination, for a denominator.

More Exercises for the Slate. 2. What part of I £. is 2 s. 6 d.

A. 2=1 3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz.?

A. 238 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. . 6. What part of 1 tun is 1 gallon, o qts. 2 pts. 1 gill?

A. site 7 What part of 15 pipes is 25 galls.? A. *s: 8. What part of 2 miles is 7 fur. 11 in. 2 b. c. ?

9. What part of 1 month is 19 days? A. 18. 10. What part of 1 month is 25 days, 13 hours ?

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

A. 338. 1 XLIX. TO REDUCE A FRACTION TO WHOLE NUM.

BERS OF LESS DENOMINATIONS, or, TO FIND THB VALUE OF A FRACTION.

1. How much is I of a shilling? How much that of a lb. ! te of a lb.? is of a !b.? it of a lb.? t of a lb.? of of 1 qr. of a cwt.? 28? 28? ? ?? an hour ?? ?

Operation by Slate illustrated. 1 What is the value of & of a pound?

20 $.

1

OPERATION.

Q. How do you pro Numer. 5

ceed in this example ! and why?

A. As 1 £. = 20 Denom. 6) 100 (16 s.

$ of one pound is the 6

name as of 20 s., ancha

to get of 20, we mul 40

tiply the numerator 5 36

and 20 together, mak

ing 100; which, divid de 8 d. Ans. 4

ed by the denominator 12

6, gives 16 s. and of

another shilling to 6) 48 (8 d. maining. This 48

of 12 d.; then, of

12 d.=8 d.
From these illustrations we derive the following

RULE.
Q. What do you multiply the numerator by!

4. By as many of the next denomination as make one of that, that is, pounds by what makes 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 I
A. Multiply and divide as before.
More Exercises for the

Slate.
2. What is the value of of a cwt.? A. 3 qrs.
3. What is the value of į of an acre ? A. I 'rood, 13} rde.
4. What is the value os 38 of a pound Troy? A. 10 02.
pwis. 1643.
5. What is the value of 313 of a hogshead? A. 49 gallons

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6. What is the valne of 3H of a pound avoirdupois? A. 1 Dan

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7. What is the value of $$$ of a bogshead? A. 50 gallona 8. What is ise value of x'g of a day? A. 16 hours, 36 inia

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(L. TO REDUCE FRACTIONS OF A HIGH ER DENOMINK

TION INTO A LOWER.

We have seen († XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce to £. to the fraction of a penny.

In this example, we multiOPERATION.

ply the 1, in o, as in ReNumer. 1

duction of whole numbers 20 s.

viz., pounds by what makes

pound, shillings by what 20

makes a shilling, &c. But 12 d.

this operation may be express

ed differently, thus ; ago X New numer. 240

20 X 12=*i= d.; or, by

dividing the denominators, Then, 240

thus; 100+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.
Reduce ato of a pound to the fractiou of a shilling.

A. TE & Reduce Tomo of a pound to the fraction of a farthing.

=fd. Ans.

A Roduce Tots of a hogshead to the fraction of a gallon.

A. T's gale Reduce Iti of a bushel to the fraction of a quart.

A. tfta Reduce TITT of a day to the fraction of a minute.

A. *** 1. Reduce TOT of a cwt. to the fraction of a pound.

A.售出, Reduce 577 of a hhd. to the fraction of a pint. A. Reduce reo of a pound to the fraction of a shilling.

TLI. TO REDUCE FRACTIONS OF A LOWER DENOMINA

TION INTO A ILIGHER.

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

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

In this example, we divide as in Ron Denom. 2

duction, (I XXIX.) viz , pence by 12

pence, shillings by shillings; but, in order for this, we inust either inultiply

the denominator or divide the numera24

tor by the same numbers that we should 20 divide by in Reduction of whole num

bers. The same result will be obtain New denom. 480 ed if performed thus : Then, Ito, Ans. x 12 x 20=To £., Ans.

Hence the following

RULE. Q. How do you proceed ? 4. Divide as in Reduction of whole numbers.

d.

More Exercises for the State. . Reduce I of a shilling to the fraction of a pound.

A. ato £ & Reduce o of a farthing to the fraction of a pound.

A. Too La 1. Reduce its of a gallon to the fraction of a hogshead.

A. Tobg bhd & Reduce 147 of a quart to the fraction of a bushel.

A. Th bai Reduce Hli of a minute to the fraction of a day.

ATT 7. Redace of a pound to the fraction of a bundred weight

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

A. 70 ਤੋਂ
Reduce t of a shilling to the fraction of a pound.

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