If fractions be of different denominations, find their value separately, and add as in compound addition.

EXAMPLES.

Note 1.-When the given fractions have a common denominator, add their numerators together and place the sum over the common denominator.

Note 2. When the given fractions have not a common denominator, reduce them to such as have, by rule in Case 2 of Reduction; then add, as in the foregoing examples.

Note 3.-When mixed numbers are given, add the fractions as under note 1 or 2; then, if their sum be an improper fraction, reduce it to a mixed number, and add its integers to the given integers; but if it be not an improper fraction, annex it to the sum of the given integers.

10. Add 53, 63, and 44 together.

Fractions.
2+1+1=224·

Result 174

Note 4.-When compound fractions are given, reduce them to single fractions, and proceed as before.

16. Add & of, and of together. Result 1

Result.

18. Add 13, 4 of 3, and 93 together. Result 11%. 19. Add 1, 63, 3 of 1, and 71⁄2 together.

Result 167

Note 5.-When the given fractions are of several denominations, reduce them to their proper values or quantities, and add as in the following example. 20. Add of a pound, to of a shilling.

Result 15s. 10, d.

SUBTRACTION OF VULGAR FRACTIONS.

GENERAL RULE.

Prepare the given fractions as in addition, then subtract the less numerator from the greater, and place the difference over the common denominator.

Note 1 When the given fractions have not a common denominator, reduce them to such as have, and then subtract as before.

Note 2.-When mixed numbers are given, reduce them to improper fractions, and reduce these improper fractions to such as have a common denominator; then subtract as before.

9. From 8 take 6

10. From 91 take 44. 11. From 7 take 3.

9

Result 134. Result 42% Result 42

Note 3.-When compound fractions are given, reduce them to single ones, and reduce these single fractions to such as have a common denominator, then subtract as before.

Note 4.-When a fraction or a mixed number is to be subtracted from a whole number, subtract the numerator of the fraction from its denominator, and under the remainder set the denominator; then carry 1 to be subtracted from the integers.

Note 5.-When the given fractions are of different denominations, reduce them to their proper values, or quantities, and subtract as in the following example.

18. From of a pound, take of a shilling.

Result 14s. 3d.

20. From

of a lb. troy, take of an ounce.
Result Soz. 16dwt. 16grs.

21. From of a yard take 3 of an inch.

22. From of a L. take of of a shilling,

Result 10s. 78. 1qr. §.

Result 5in. 3.

MULTIPLICATION OF VULGAR FRACTIONS.

GENERAL RULE.

Reduce compound fractions to single ones, and mixed numbers to improper, fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator.

EXAMPLES.

1. Multiply by . 2. Multiply by . 3. Multiply by 18.

Results. Result Result 224.

10. Multiply of 7 by 3.

11. Multiply 23 by 14, and multiply the product by

of of 4.

Result.

DIVISION OF VULGAR FRACTIONS.

GENERAL RULE.

Prepare the given fractions, if necessary, then invert the divisor, and proceed as in Multiplication.