སྐ

(7) Reduce to the lowest terms.

115960

(8) What are the lowest terms of 198?

Case 2. To reduce an improper fraction to its equivalent

number.

RULE. Divide the upper term by the lower.

This is evident from Definition 3.

69

Ans. 13.

(1) Reduce 189 to a mixed number. 149=18%. Ans.
(2) Reduce to its equivalent number.
(3) Reduce 245 to its equivalent number.
(4) Reduce 1245 to its equivalent number.
(5) Reduce 349 to its equivalent number.
(6) Reduce 1 to its equivalent number.

Ans. 273. Ans. 561. Ans. 1832.

Ans. 7118.

Case 3. To reduce a mixed number to an improper fraction.* RULE. Multiply the whole number by the denominator of the fraction, and to the product add the numerator for the numerator required, which place over the denominator.

NOTE. Any whole number may be expressed in a fractional form, by putting for the denominator: thus 11 = Y·

=

(1) Reduce 18% to the form of a fraction.† (2) Reduce 5613 to an improper fraction.

A number is a multiple of 11, when the sum of the 1st. 3rd. 5th. &c. digits that of the 2nd. 4th. 6th. &c. digits, after retrenching the

elevens contained in each.

A multiple of both 2 and 3, is, of course, a multiple of 6; and a multiple of 3 and 4, may be divided by 12.

All prime numbers, except 2 and 5, have 1, 3, 7, or 9, in the units' place: all others are composite.

(3) Reduce 183 to an improper fraction.
(4) Reduce 13 to its equivalent fraction.
(5) Reduce 27% to its equivalent fraction.
(6) Reduce 514 to a fractional form.

16

Case 4. To reduce a fraction to another of the same value, having a certain proposed numerator or denominator.

RULE. As the present numerator, is to the denominator ; so is the proposed numerator, to its denominator. Or, as the present denominator, is to the numerator; so is the proposed denominator, to its numerator.

(1) Reduce to a fraction of the same value, whose numerator shall be 12. As 23 12: 18. Ans. 1. (2) Reduce to a fraction of the same value, whose numerator shall be 25. Ans.. (3) Reduce to a fraction of the same value, whose numerator shall be 47.

Ans. 47

654.

(4) Reduce to a fraction of the same value, whose denominator shall be 18.

Ans. 1

to a fraction of the same value, whose deAns.

(5) Reduce

nominator shall be 35.

(6) Reduce to a fraction of the same value, whose denominator shall be 19.

Ans.

168

19.

Case 5. To reduce complex and compound fractions, to a

simple form.

RULE. For a complex fraction, reduce both terms to simple fractions then by inverting the lower fraction, they may be considered as the terms of a compound fraction. And to reduce a compound fraction, arrange all the numerators above a line, and the denominators below, with the signs of multiplication interserted: divide all the upper and lower terms that are commensurable,* cancelling them with a dash,... and placing their quotients above and below them respectively. Do the same with the quotients: then the products of the uncancelled numbers will give the single fraction in its lowest terms.t

* That is, having a common divisor.

+ This rule is of the highest importance as tending to expedite the bu

siness of computation, by abbreviating to the utmost all fractional expressions, as we proceed."

EXAMPLES.

(2) Reduce of of of to a simple fraction.

(3) Reduce the annexed fractional expression to its proper quan

tity.

16×1452× 1×72× 25× 98×13×567 77

11× 108×13×18×147×320×15× $4 32

L.

= =23

1

1

221 20 3 8

1 3 4 1

= £2..8}s.= £2..8..14. Ans. 1

(7) Reduce }} of 183
1418

128

91

28

Ans. 13.

16

of to a simple fraction.
383

(8) Reduce of of 11 to a single fraction. Ans. 18.
of 37 of 5 to its equivalent number.
Ans. 1124.
to its equivalent number.
Ans. 7.

(9) Reduce (10) Reduce 1

of 25% of

236

14

Case 6. To reduce a fractional quantity of a given denomi nation, to an equivalent fraction of another denomination.

RULE. Consider what numbers would reduce the greater denomination to the less; then to reduce to a greater name, multiply the denominator by those numbers, and to reduce to a less name, multiply the numerator: the compound thus produced, when reduced to a simple form, will be the fraction required.

(1) Reduce of a penny to the fraction of a pound.*
(2) Reduce d. to the fraction of a crown. Ans. go cr.
(3) Reduce dwt. to the fraction of a lb. troy. Ans. zžō lb.
(4) Reduce 4 lb. avoirdupois to the fraction of a cwt.
Ans. cwt.
(5) Reduce of a pound to the fraction of a penny.†
(6) Reduce go to the fraction of a penny. Ans. d.
of a pound troy to the fraction of a pen-
Ans. dwt.
#

(7) Reduce

(8) Reduce

ny-weight.

1920

cwt. to the fraction of a lb. Ans. lb. Case 7. To find the proper value of a fractional quantity. RULE. Reduce the numerator to such lower denomination as may be necessary, and divide by the denominator; abbreviating as much as possible in valuing the remainders.

NOTE. It is evident, from Definition 3, that this Case is precisely that of Compound Division.

(1) Reduce of a pound sterling to its proper value.‡

Ans. 6 fur. 105 yds.
proper value.
Ans. 1 a. 2 r. 31 per.
Ans. 1 gr. 22 lb. 333.

(10) Find the value of 1 cnt.

Case 8. To reduce any given quantity to the fraction of a greater denomination.

RULE. Reduce the given quantity (if compound) to the lowest denomination mentioned, that it may assume a simple form: then multiply the denominator as in Case 6.

(1) Reduce 15s. to the fraction of a pound sterling.

15s.=£}}=£3. Ans. (2) Reduce 4d. 33 qrs. to the fraction of a shilling. Ans. 3. (3) Reduce 9 oz. 2 dr. to the fraction of a lb. avoirdu

Ans. lb.

pois.
(4) Reduce 3 qrs. 33 lb. to the fraction of a cwt.

Ans. cwt.

(5) Reduce 7 oz. 4 dwts. to the fraction of a lb. troy.

Ans. lb.

(9) What fraction of an acre are 3 roods, 32

29

cr.

Ans. £11. crown. Ans. 90 perches ? Ans. 12 a. Ans. s.

(10) What part of a shilling are of 2d. Case 9. To find the least common multiple of two or more

numbers.

RULE. Arrange the given numbers in a line, (omitting any one that is a factor of one of the others) and divide any two or more of them by a common divisor, placing the quotients and