Imágenes de páginas
PDF
EPUB

5. Divide 14 by fi: A. 33.
6. Divide 94 by 1 of . A. 37.
7. How many times is of contained in 1 ? A. 13.
8. How many times is it contained in 1 ? A. 2154.
9. What number multiplied by & will make 15? A. 214.

[merged small][ocr errors][ocr errors]

REDUCTION OF FRACTIONS. It will be recollected, that in Reduction (9 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.

[merged small][ocr errors]

1 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 qrs.? Is 3 qrs.? 13. What part of 1 s. is 1 d.? Is 2 d.? Is 3 d.?

[merged small][merged small][merged small][ocr errors]

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

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

3 pks. 4 qts.=28 qts. 4

Then, as 32 qts. make

1 bushel, 1 qt. is 32 24

of a bushel, and 28 qts. 8

4

28 times =) 32 Denom. 28 Numer.

Abu: Ans., the same

as before. Then =, Ans.

mark

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.

More Exercises for the Slate. 2. What part of 1 £. is 2 s. Cd.

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

4. What part of 1 yard is 3 qrs.

3 na.

? A. 16 5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt. ?

A. 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. I gill?

4. gr. 17. What part of 15 pipes is 25 galls.? A. 38 8. What part of 2 miles is 7 fur. 11 in. 2 b. c.?

A. 483370 9. What part of 1 month is 19 days? A. 18. 10. What part of 1 month is 25 days, 13 hours ?

A. 413. 11. What part of 1 month is 22 days, 15 h. 1 min.?

A. 1387.

T XLIX. TO REDUCE A FRACTION TO WHOLE NUM

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

THE

1. How much is 1 of a shilling? How much I of a lb. ? Po of a lb.? 16 of a lb.? H of a lb.? 19 of a lb.? as of 1 qr. of a cwt.? ? ? 15? ? an hour ? ? ?

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

20 s.

[ocr errors]

OPERATION.

Q. How do you proNumer. 5

ceed in this example ?
and why?

A. As 1 £.
Denom. 6) 100 (16 s.

of one pound iš the 6

same as of 20 s., and,

to get & of 20, we mul40

tiply the numerator 5 36

and 20 together, mak

ing 100; which, divid16 s. 8 d. Ans. 4

ed by the denominator 12

6, gives 16 s. and of

another shilling re6) 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?

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 of a cwt. ? A. 3 qrs. 3. What is the value of j of an acre ? A. 1 rood, 134 rds.

4. What is the value of 2% of a pound Troy? A. 10 oz. 8 pwts. 1619.

5. What is the value of 213 of a hogshead ? A. 49 gallons 12973 qts.

6. What is the value of 37 i of a pound avoirdupois ? A. 1 lb. 14971 oz.

7. What is the value of 530 of a hogshead? A. 50 gallons.

8. What is the value of 13 of a day? A. 16 hours, 36 min. 553 sec.

I L. TO REDUCE FRACTIONS OF A HIGHER DENOMINA

TION INTO A LOWER. We have seen (1 XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce 450 £. to the fraction of a penny.

In this example, we multi OPERATION.

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

duction of whole numbers, 20 s.

viz., pounds by what makes á

pound, shillings by what 20

makes a shilling, &c. But 12 d.

this operation may be express

ed differently, thus ; 450 X New numer. 240

20 X 12=4=fd; or, by

dividing the denominators, Then, 240

thus; Ito-20=212 =fd. Ans. 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 to of a pound to the fraction of a shilling.

A. s. 3. Reduce 1927 of a pound to the fraction of a farthing.

A. gr.

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

A. Te gal. 6. Reduce Th of a bushel to the fraction of a quart.

A. 141 qt. 6. Reduce 144T of a day to the fraction of a minute.

A. 144 m. 7. Reduce to y of a cwt. to the fraction of a pound.

A. 1b. 8. Reduce zoo of a hhd. to the fraction of a pint. A. $ pt. 9. Reduce Igo of a pound to the fraction of a shilling.

Ă. Ja

FLI. TO REDUCE FRACTIONS OF A LOWER DENOMINA

TION INTO A HIGIER.

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

This rule is the reverse of the last, (1 L.) and proves it.
1. Reduce } of a penny to the fraction of a pound.
OPERATION. In this example, we divide as in Re-
Denom. 2

duction, (1 XXIX.) viz., pence by

pence, shillings by 'shillings; but, in 12

order for this, we must either multiply

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 obtainNew denom. 480 ed if performed thus :

d. Then, to, Ans. 3 x 12 x 20=45o £., Ans.

Hence the following

RULE. Q. How do A. Divide as in Reduction of whole numbers.

[ocr errors]

you procitor?

More Exercises for the Slate. 2. Reduce I of a shilling to the fraction of a pound.

A. ato £. 3. Reduce 1 of a farthing to the fraction of a pound.

A. 1927 £. 4. Reduce It of a gallon to the fraction of a hogshead.

A. Toto hhd. 5. Reduce 14 i of a quart to the fraction of a bushel.

A. I bu. 6. Reduce 1441 of a minute to the fraction of a day.

A. 1441 7. Reduce of a pound to the fraction of a hundred weight.

A. Toor: 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. .

[ocr errors]
« AnteriorContinuar »