246. To reduce fractions to integers of a lower denomination, and the reverse.

integers of a lower denomina-fractions of a higher denomination.

RULE.-Reduce the numer

tion.

RULE. Reduce the given ator to the next lower denom- number to the lowest denomiination, and divide by the de-nation mentioned for a numernominator; if there be a re-ator, and a unit of the higher mainder, reduce it still lower, denomination to the same for and divide as before; the sev- a denominator of the fraction cral quotients will be the an- required.

swer.

QUESTIONS FOR PRACTICE.

2. In of a day, how many hours?

3. In of an hour, how many minutes and seconds? 4. In 2 of a mile, how many rods?

5. In of an acre, how many roods and rods? 9 *

2. What part of a day are 8 hours?

3. What part of an hour are 6m. 40s. ?

4. What part of a mile are 120 rods?

5. What part of an acre are 1 rood and 30 rods?

249. ADDITION OF FRACTIONS.

ANALYSIS.

1. What is the sum of of a dollar and of a dollar? As both the fractions are 9ths of the same unit, the magnitude of the parts is the same in both-the number of parts, 3 and 4, may therefore be added as whole numbers, and their sum, 7, written over 9, thus, I, expresses the sum of two given fractions.

2. What is the sum of of a yard and of a yard?

As the parts denoted by the given fractions are not similar, we cannot add them by adding their numerators, 3 and 2, because the answer would be neither & nor; but if we reduce them to a common denominator, becomes, and, (240). Now each fraction denotes parts of the same unit, which are of the same magnitude, namely, 24ths; their numerators, 8 and 9, may therefore be added; and their sum, 17, being written over 24 we have of a yard for the sum of and of a yard.

250. To add fractional quantities.

RULE.-Prepare them, when necessary, by changing compound fractions to single ones (224), mixed numbers to improper fractions (218), fractions of different integers to those of the same (247,248), and the whole to a common denominator (240); and then the sum of the numeraters written over the common denominator, will be the sum of the fractions required.

251. SUBTRACTION OF FRACTIONS.

ANALYSIS.

1. What is the difference between of a dollar and of a dollar?

difference.

evidently expresses 2 tenths more than 3 tenths; then is the of a yard and g of a

2. What is the difference between yard?

Here we cannot subtract from, for the same reason that we could not add them (49). We therefore reduce them to a common denominator, (24 24), and then the difference of the numerators (9-8-1), written over 24, the common denominator, gives for the difference of the fractions. RULE. Prepare the fractions as for addition (250), and then the difference of the numerators written over the common denominator will be the difference of the fractions required.

252. RULE OF THREE IN VULGAR FRACTIONS.

RULE.-Prepare the fractions by reduction, if necessary, and state the question by the general rule (198); invert the first term, and then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator; the new numerator, written over the new, denominator, will be the answer required.

QUESTIONS FOR PRACTICE.

1. If oz. cost £7, what is tyd. wide, will line 131 will loz. cost? yards of cloth that is 2 yds.

oz. £ oz.

wide?