EXAMPLES FOR PRACTICE.

Reduce the following to improper fractions:

21. How many fourteenths in 92? In 210? In 763? 22. Reduce 54 to an improper fraction whose denominator is 65; 73; 84.

94. TO REDUCE FRACTIONS TO THE LEAST COMMON DENOMINATOR.

EXAMPLE.-Reduce,, and to the least common

CONCLUSION.―Therefore,,, and, reduced to the least common denominator, equal,, and. Hence, the

Rule. Find the least common multiple of the denominators of the given fractions; and multiply both terms of each fraction by the quotient of the least common mul tiple divided by the denominator of the fraction

NOTE.-Each fraction should be reduced to its lowest terms before commencing the operation, and all mixed numbers to improper fractions.

Reduce the following to their least common denom. inator:

ADDITION OF FRACTIONS.

95. Addition of Fractions is the process of collect ing two or more fractional quantities into one sum. EXAMPLE.-What is the sum of 3 and ??

SOLUTION. Since quantities of the same denomination only, can be added, first reduce the fractions to a common denominator.

equal, and equal. As they are now of the same denomination, they can be added; 13, and reducing to a

mixed number, 12 = 11⁄2·

OPERATION.

=

12,

&+&=};

1=12, Ans

'the

CONCLUSION.-Therefore, the sum of and is 15. Hence,

Rule.-Reduce the fractions to a common denominator; add their numerators, and place the sum over the common denominator.

NOTE.-After adding, reduce the result to its lowest terms.

EXAMPLES FOR PRACTICE.
1. What is the sum of 3, 4, §, 7, and 1?
2. What is the sum of,,, §, and ?
3. What is the sum of, 4, 1, 24, and 7?

17

1

4. Add 18, 4, 3, and 17.

81

5. Add 1, 2, 1, and 12.
19
끊,,

532.

6. Add 2, 1, 2, 7, and 17.

NOTE.-Mixed numbers may be reduced to improper fractions, And then added; or, the whole numbers and fractions may be dded separately, and their sums united.

7. Add 61, 131, 18%, and 311. 8. Add 274, 413⁄43, 191⁄2, and 47§. 9. Add 16, 123, 83, and 24. 10. Add 12, 63, 9, and 53. 11. Add †, ¿, †, §, and †.

12. Add 14, 1†, 13, 11⁄21⁄2, and 34. 10

R. A.

SUBTRACTION OF FRACTIONS.

96. Subtraction of Fractions is the process of find ing the difference between two fractional quantities. EXAMPLE.-What is the difference between 3 and §?

SOLUTION. Since quantities of the same denomination only, can be subtracted, first reduce the fractions to a common denominator. 3=2, and 3=2. As they are now of the same denomination, they can be subtracted; 35-27=

OPERATION.

# — 4 = &, Ans.

CONCLUSION.-Therefore, the difference between and is ਕੰਨ Hence, the

Rule.-Reduce the fractions to a common denominator, find the difference of their numerators, and place it over the common denominator.

MENTAL EXERCISES.

1. Subtract from
2. Subtract from .
3. Subtract from H.

4. Subtract

from 8.

5. Subtract from 2. 6. Subtract 48 from 18. and .

7. Required the difference between

15. Required to find the difference between 31

and 13.

NOTE.-Mixed numbers may be reduced to improper fractions, and then subtracted; or the whole numbers and fractions may be subtracted separately, and the results united.

16. From 4 subtract 1.

17. From 31 subtract 21. 18. From 12 subtract 61

22. A farmer had 123 A. of land; he bought 374 A., and gave his son 49 A.: how much had he left?

MULTIPLICATION OF FRACTIONS.

97. Multiplication of Fractions is the process of multiplication, when one or both of the factors are fractional numbers. It embraces three cases

Case I. To multiply a fraction by a whole number.
EXAMPLE.-What is the product of

by 4?

SOLUTION.-The multiplicand

is to be taken four times. Since
the numerator 3, indicates the num-
ber of parts, the fraction will be
multiplied by multiplying the nu-
merator; 4 times 3 fifths 12 fifths;
and, reducing to a mixed number, 1222.

=

multipled

OPERATION.

× 4 = y,
',

12 = 23, Ans.

CONCLUSION.-Therefore, the product of multiplied by 4 is 23. Hence, the

Rule.-Multiply the numerator of the fraction by the whole number, and place the result over the lenominator.