183. To reduce the fraction of a less denomination to that of

a greater, retaining the same value.

RULE. Multiply the denominator by all the denominations between that which is given and that which is required; over the product place the given numerator, and you will have the fraction required *.

I multiply the denominator 9 by 12 and 20, (because 12 pence make a shilling, and 20 shillings a pound,) and place the numerator 8 over, which gives

99. Reduce

of a penny to the fraction of a pound.

This rule is equivalent to that for reducing a compound fraction to a

4

5

100. Reduce of a penny to the fraction of a guinea.

9

101. Reduce of a nail to the fraction of a yard. An

10

102. Reduce 78

of a square pole to the fraction of an acre.

of a bushel of coals to the fraction of a chal

chaldron.

54

104. Reduce

9 10

of a day to the fraction of a year. An

184. To reduce the fraction of a greater denomination to that of a less, retaining the same value.

RULE. Multiply the numerator by all the denominations between the given one and that which is required; under the product place the given denominator, and it will give the frac tion required".

105. Reduce of a pound to the fraction of a penny.

1 270

I multiply the numerator 1 by 20 and 12, (the denominations between pounds and pence,) and place the denominator 270 under the product, making 8

the fraction which reduced to its lowest terms gives

240
270

9

This rule is likewise of the same nature with Art. 175, for its operation is simply the reducing a compound fraction to a simple one; thus (ex. 105.)

20 12

of a pound is of of of a penny, or 270 270 1 rule is evident.

1 X 20 X 12

; wherefore the

270

1

106. Reduce of a pound troy to the fraction of a grain.

7200

2 of a cwt. to the fraction of a lb. Ans. lb. 3

185. To reduce compound numbers, &c. in money, weights, and measures, to fractions of some higher denomination.

RULE I. Reduce the given number to the lowest denomination mentioned for a numerator.

II. Reduce the integer of which the above is to be made a fraction into the same denomination for a denominator.

III. Place the numerator over the denominator, and reduce the fraction to its lowest terms. Art. 170.

In ex. 112, 3s. 6d. = 42 pence, and il. 240 pence; therefore 3s. 6d. is 42 parts out of 240 of a pound; whence the reason of this process is plain. It is best to reduce the given number, and the integer of which it is to be made à fraction, to the greatest denomination common to both; for then the fraction will be in its lowest terms. Thus (ex. 112.) 3s. 6d. 7 sixpences,

1=

and 17. 40 sixpences; therefore 3s. 6d.

7

l. as in the example.

112. Reduce 3s. 6d. to the fraction of a pound.
Thus, 3s. 6d. = 42 pence, the numerator.
And 1 pound = 240 pence, the denominator.

113. Reduce 14s. 6d. to the fraction of a guinea.

Thus, 14s. 6d. 349 halfpence, the numerator.
And 1 guinea =504 halfpence, the denominator.

349

Therefore 14s. 6d. = of a guinea, Ans.

504

114. Reduce 1oz. 2dwts. to the fraction of a lb. troy. Thus, 1oz. 2dwts. = 22dwts, the numerator.

And 1lb. 240dwts. the denominator.

115. Reduce 1lb. 2oz. 34dr. to the fraction of a lb.

Thus, 1lb. 2oz. 34dr. = 583 half drams, numerator.
And 1lb. 512 half drams, denominator.

116. Reduce 12s. to the fraction of a pound.

3
Ans. L.
5

39

117. Reduce 19s. 6d. to the fraction of a pound. Ans. L.

40

118. Reduce 3qrs. 14lb. to the fraction of a cwt.

119. Reduce 3qrs. 3n. to the fraction of an

120. Reduce 1hhd. 2gal. 3qts. to the fraction of a tun.

121. Reduce 3bu. 24pks. to the fraction of a quarter.

122. Reduce 10bu. 3pks. to the fraction of a chaldron

43

Ans.

chaldron.

123. Reduce 12w. 3d. 4h. 5m. 6" to the fraction of a year of

196. To find the value of a fraction in the known parts of

the integer.

RULE I. Reduce the numerator to the next lower denomination, divide the result by the denominator, and the quotient will be of the said lower denomination.

II. Reduce the remainder to the next denomination lower than the last, divide the result by the denominator, and the quotient will be of this last denomination.

III. Proceed in this manner until you arrive at the lowest denomination, then collect all the quotients together for the answer f

I reduce the numerator 7 to shillings, viz. 140; this I divide by the denominator 8, and the quotient is 17, and 4 over; 4 shillings are 48 pence, eights in 48 will go 6 times.

f Since the numerator is less than the denominator, the former may be considered as a remainder, and the latter as a divisor; whence the rule has its reason in the nature of compound division, where every remainder is reduced to the next lower denomination, and being then divided, produces integers of the said denomination. See Art. 108 to 124.