¶ 62. From the foregoing examples we derive the following RULE:-To add or subtract fractions, add or subtract their numerators, when they have a common denominator; otherwise, they must first be reduced to a common denomi

nator.

Note. Compound fractions must be reduced to simple fractions before adding or subtracting.

EXAMPLES FOR PRACTICE. 1., What is the amount of 4, 44 and 12? 2. A man bought a ticket, and sold of the ticket had he left?

3. Add together,,,,t and 1. 4. What is the difference between 14

5. From 1 take 2.

6. From 3 take §.

7. From 147 take 484.

8. From of take of.

Ans. 17.

of of it; what part

Ans..

Amount, 228.

and 167?

Ans. 118.

Remainder, .

Rem. 23.

Rem. 988.

Rem. .

and 1.

9. Add together 112, 311, and 1000g. 10. Add together 14, 11, 4,

11. From take. From take †.

12. What is the difference between and ? and? and? and ? and ? and ??

13. How much is 1.

? 1-4? 1-f? 1-f? 2-4? 2—4? 24-3? 34-? 1000-o?

REDUCTION OF FRACTIONS.

¶ 63. We have seen, (T 33,) that integers of one denomination may be reduced to integers of another denomination. It is evident, that fractions of one denomination, after the same manner, and by the same rules, may be reduced to fractions of another denomination; that is, fractions, like integers, may be brought into lower, denominations by mul tiplication, and into higher denominations by division.

To reduce higher into LOWER To reduce lower into HIGHER

denominations.

(RULE. See T 34.):

penny.

denominations.

(RULE. See T34.)

1. Reduce of a pound 2. Reduce of a penny to to pence, or the fraction of a the fraction of a pound. Note. Division is performNote. Let it be recollect- ed either by dividing the nued, that a fraction is multiplied merator, or by multiplying the either by dividing its denomi- denominator. nator, or by multiplying its nu- d.

merator.

Or thus: of 20 of 12 = 348 of a penny, Ans.

12s.÷20

zo £. Ans.

3. Reduce 12 of a pound 4. Reduce of a farthing to the fraction of a farthing. to the fraction of a pound. 1280 £. X 20=8S. X & q. ÷ 4 = √ d. ÷ 12 — 12=24 d. X 4 = 1280 = 1329208402NO£.

ૐ q.

80

Or thus:

Num. 1

960

Or thus:
Denom. 4

4 q. in 1 a.

10. Reduce of a guinea

9. Reduce of a moidore, at 36 s. to the fraction of a guinea. to the fraction of a moidore. 11. Reduce of a pound, 12. Reduce of an ounce Troy, to the fraction of an to the fraction of a pound

ounce.

1

Troy.

L*

13. Reduce of a pound, 14. Reduce

of an ounce

avoirdupois, to the fraction of to the fraction of a pound

an ounce.

15. A man has of a

avoirdupois.
16. A man has

of a pint

.hogshead of wine; what part of wine; what part is that of

is that of a pint?
17. A cucumber grew to the
of a mile; what

length of

part is that of a foot?

of a shilling is of

19. Reduce of of a 20. pound to the fraction of a shil-what fraction of a pound?

ling.

21. Reduce of of 3 pounds to the fraction of a penny.

22. 180 of a penny is of what fraction of 3 pounds? 180 of a penny is of what part of 3 pounds? 180 of a penny is of of how many pounds?

¶ 64. It will frequently be It will frequently be rerequired to find the value of a quired to reduce integers to fraction, that is, to reduce a the fraction of a greater defraction to integers of less de- nomination.

nominations.

1. What is the value of 2. Reduce 13 s. 4 d. to the of a pound? In other words, fraction of a pound. Reduce of a pound to shil- 13 s. 4 d. is 160 pence; lings and pence. there are 240 pence in a of a pound is 40133 shil-pound; therefore, 13 s. 4 d. is lings; it is evident from of 18 of a pound. That a shilling may be obtained is,-Reduce the given sum or some pence; of a shilling is quantity to the least denomina24 d. That is,-Multiply tion mentioned in it, for a nuthe numerator by that number merator; then reduce an intewhich will reduce it to the next ger of that greater denominaless denomination, and divide tion (to a fraction of which it the product by the denominator; is required to reduce the givif there be a remainder, multiply en sum or quantity) to the and divide as before, and so on; same denomination, for a denomithe several quotients, placed one nator, and they will form the after another, in their order, fraction required.

will be the answer.

6. Reduce 7 oz. 4 pwt. to the fraction of a pound Troy.

8. Reduce 8 oz. 14 dr. to the fraction of a pound avoirdupois.

Note. Both the numerator and the denominator must be reduced to 9ths of a dr.

9. of a month is how many days, hours, and minutes? is 11. Reduce of a mile to its proper quantity.

13. Reduce of an acre to its proper quantity.

15. What is the value of of a dollar in shillings, pence, &c.?

17. What is the value of of a yard?

19. What is the value of of a ton ?

10. 3 weeks, 1 d. 9 h. 36 m. what fraction of a month? 12. Reduce 4 fur. 125 yds. 2 ft. 1 in. 24 bar. to the fraction of a mile.

14. Reduce 1 rood 30 poles to the fraction of an acre.

16. Reduce 5 s. 7 d. to the fraction of a dollar.

18. Reduce 2 ft. 8 in. 14b. to the fraction of a yard.

20. Reduce 4 cwt. 2 qr. 12 lb. 14 oz. 12 dr. to the frac tion of a ton.

Note. Let the pupil be required to reverse and following examples:

21. What is the value of of a guinea?

prove the

22. Reduce 3 roods 17 poles to the fraction of an acre. 23. A man bought 27 gal. 3 qts. 1 pt. of molasses; what part is that of a hogshead?

24. A man purchased of 7 cwt. of sugar; how much sugar did he purchase?

25. 13 h. 42 m. 514 s. is what part or fraction of a day?

SUPPLEMENT TO FRACTIONS.

QUESTIONS.

a

1. What are fractions? 2. Whence is it that the parts into which any thing or any number may be divided, take their name? 3. How are fractions represented by figures? 4. What is the number above the line called?—Why is it so called? 5. What is the number below the line called? -Why is it so called?-What does it show? 6. What is it which determines the magnitude of the parts ?-Why? 7. What is a simple or proper fraction? an improper fraction? a mixed number? 8. How is an improper fraction reduced to a whole or mixed number? 9. How is a mixed number reduced to an improper fraction? whole number? 10. What is understood by the terms of the fraction? 11. How is a fraction reduced to its most simple or lowest terms? 12. What is understood by a common divisor? - by the greatest common divisor? 13. How is it found? 14. How many ways are there to multiply a fraction by a whole number? 15. How does it appear, that dividing the denominator multiplies the fraction? 16. How is a mixed number multiplied? 17. What is implied in multiplying by a fraction? 18. Of how many operations does it consist? What are they? 19. When the multiplier is less than a unit, what is the product compared with the multiplicand? 20. How do you multiply a whole number by a fraction? 21. How do you multiply one fraction by another? 22. How do you multiply a mixed number by a mixed number? 23. How does it appear, that in multiplying both terms of the fraction by the same number the value of the fraction is not altered? 24. How many ways are there to divide a fraction by a whole number?-What are they? 25. How does it appear that a fraction is divided by multiplying its denominator? 26. How does dividing by a