Case V.-To reduce fractions to their least common

denominators.

RULE. Find the L. C. M. of all the denominators, for the least common denominator; and multiply each fraction in succession by the quotient obtained by dividing this common denominator by the denominator of each fraction.

EXAMPLE 1.-Reduce,,, and to equivalent fractions having a common denominator.

NOTE.-Where necessary reduce each fraction to its lowest terms before commencing to find the least common multiple.

EXAMPLE 2.-Reduce, &, to their least common deno

Case VI. To reduce a compound to a simple fraction. RULE.-Multiply all the numerators together for a new numerator, and all the denominators for a new denominator, previously cancelling all the factors that are common to a numerator and a denominator of any of the compound fractions. EXAMPLE 1. Reduce of 27 of 18 of to a simple

fraction.

of

13 x 5 65

NOTE.--If any term of the fraction be a mixed number, it must be reduced to its equivalent improper fraction before applying the rule. EXAMPLE 2.-Reduce 23 of 4 of 2 of 23

to a simple fraction

ADDITION OF FRACTIONS.

RULE. Reduce the fractions to their least common denominator by Case V.; add the numerators together for a new numerator; and beneath their sum write the common denomi

NOTE.-Compound fractions must be reduced to simple ones before com. mencing to reduce them to a common denominator. When mixed numbers occur the whole numbers may be added separately from the fractional parts.

EXAMPLE. Find the value of 211 + 351

5+ of 7.

SUBTRACTION OF FRACTIONS.

RULE--Reduce the fractions to a common denominator;

subtract the less numerator from the greater; and under the remainder write the common denominator.

NOTE.-As in addition of fractions, compound fractions must be reduced to simple fractions; and mixed numbers must be reduced to improper fractions.

EXAMPLE 2.-From 1692 take 2317.

1694 - 2317 = 169,12 EXAMPLE 3. From of take

23138 =

145 Ans.

of 5.

5

=

1 5 1 x 5

= and of =

8 9 8 x 9

72

21. 4 of 6 of 7

40

=

72

72

EXAMPLE 4.-Find the value of 16g

89 of 11.

79

8 + 17.

L. C. M. of 8, 10, 12 = 120.

Plus quantities, 16 + 12,

of 29.

or,

16,7% + 1127

=

18,25.

Minus quantity,

36 8-380 120.

Then 18120
25 -

8120 = 9198 Ans.

+ 11

.

(34)

28.7+45 72 +31-511. 32. of of 16

+151-37.

27. 181

29. 8-69

(33)

£ 8. d.

11 + 79

100 14 8
15 18 10

£ 8. d. 18 12 9 10 14 512

MULTIPLICATION OF FRACTIONS.

RULE.-Multiply all the numerators together for a new numerator, and all the reduced denominators together for a new denominator.

NOTE-Before applying the rule, reduce all mixed numbers to improper fractions, and compound fractions to simple ones. And cancel all factors common to the numerator and denominator. Reduce the result, if necessary, to a mixed number,