SUBTRACTION OF VULGAR FRACTIONS.

RULE.

Prepare the fractions, when necessary, as directed in Addition, then subtract the one numerator from the other; place the common denominator under the difference, and this new fraction will be the difference between the given fractions*.

When a proper fraction, or a mixed number, is to be sub tracted from an integer, take the numerator of the fraction from the denominator, and place the remainder above the denominator, and diminish the minuend by one; or carry one to the right hand figure of the subtrahend, if it be a mixed number.

*The reason of the operations in this rule, and Addition, will be evident, if the numerators of the fractions be placed in a column, like the lower denomination of an integer, and then adding or subtracting them as integers, and carrying and borrowing, when necessary, accord, ing to the value of the higher denomination.

MULTIPLICATION

OF VULGAR FRACTIONS.

RULE I.

Reduce mixed numbers to improper fractions, if there be any given; then multiply all the numerators together for the numerator of the product, and all the denominators together for the denominator of the product*.

When whole numbers are multiplied together, their value is increased, or the product is greater than either of the factors; but when proper fractions are moltiplied together, their product is less than either factor; for fractions that are to be multiplied together, are, virtually, compound fractions; and are, therefore, fractions of fractions, and must, of necessity, be less than the fractions of which they are a part.

Thus, multiplied by, is the same as of, or 1, by Case 6th, which is, in effect, the same as the Rule.

RULE II.

1. To multiply a mixed number by a whole number, multiply the numerator and then the integer, carrying one to the integer for every time the denominator is contained in the product of the numerator by the multiplier.

2. To multiply a fraction by a whole number, divide the denominator of the fraction, if it can be done, which is the same, in effect, as multiplying the numerator.

11. Multiply 85% by 9%.

12. What cost 7 yards of cloth, at £3 per yard. ?

13. What cost 11

yards of ditto, at 24 guineas per yard. ?

14. What cost 173cwt. at £5 per cwt. ?

15. What cost 44 oz. troy of gold, at £3; per oz. ?

DIVISION OF VULGAR
FRACTIONS.

RULE.

Reduce mixed numbers, and compound fractions, to simple fractions, if there be any given; then invert the terms of the divisor, and multiply the dividend by it, as in Multiplication.