4. Reduce 70z. 4pwt. to the fraction of a lb. Troy.

Anf. 3lb.

5. Reduce 2qrs. 23n, to the fraction of a yard.

6. Reduce 18s. to the fraction of a guinea.

Anf. Hyd

Anf. G.

7. Reduce 5's. 71d. to the fraction of a dollar.

Anj. dol.

8. Ředuce 218. 73d. to the fraction of a moidore.

Anf. 3moid.

ADDITION OF VULGAR FRACTIONS.

RULE.

Reduce compound fractions to fingle ones; mixed numbers to improper fractions; fractions of different integers to thofe of the fame; and all of them to a common denominator; then the fum of the numerators written over the common denominator will be the fum of the fractions required.

EXAMPLES.

1. Add 7, of 3 and 7 together. First. 7, of 3=33 and 7=4.

39

39 15

Then the fractions are 3,; and ; therefore

2. What is the fum of of 44, of and 94 ?

3. Add 1. s. and d. together.

4. Add of a week, of a day, of a minute together.

Anf. 128.

Anf. 25. 8d.

of an hour, and

Anf. 2 days, 2 hours, 30 minutes, 45 seconds.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

Prepare the fractions as in Addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required-Note, a fraction is fubtracted from a whole number, by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

* In fubtracting mixed numbers, when the lower fraction (the fubtrahend) is greater than the upper one (the minuend) you may, without reducing them to improper fractions, sub. tract the numerator of the fubtrahend from the common denominator, and to that difference add the numerator of the minuend, and carry one to the integer of the subtrahend.

EXAMPLE.

From 19 take 127.19-127=61.

Reduce compound fractions to fimple ones, and mixed numbers to improper fractions; then the product of the numerators will be the numerator, and the product of the denominators, the denominator of the product required. -Note, where feveral fractions are to be multiplied, if the numerator of one fraction be equal to the denominator of another, their equal numerators and denominators may be omitted.

EXAMPLES.

1. What is the continued product of 4, 3, of,

Z !

13

3. Multiply 54 by .

4. Multiply of 5 by 4 of 4.

H

DIVISION OF VULGAR FRACTIONS.

RULE

Prepare the fractions as before; then, invert the divifor and proceed exactly as in Multiplication: The prodacts will be the quotient required.

Decimal Fractions are of fuch a nature, they they vary in the fame proportion, and are managed by the fame method of operation, as whole numbers are.

On this account, every proper fraction is supposed to be reducible to another, whose denominator fhall be 10, 100, 1000, &c. viz. Unity with a number of cyphers annexed; and fractions with such denominators, are called Decimal Fractions : Such are, too, food, &c.

675

As

To multiply a fraction by an integer, divide the denominator, or multiply the numerator by it; and to divide by an integer, divide the numerator, or multiply the denominator by it..

As the denominator of a decimal fraction is always 10, or 100, or 100 o, &c. the denominators need not be expreffed: For the numerator only may be made to exprefs the true value. For this purpofe it is only required to write the numerator with a point before it at the left hand, to diftinguish it from a whole number, when it confifts of fo many figures as the denominator hath cyphers annexed to unity, or 1: So fo is written,5; 1,33; To8,735, &c.

33

Note. The point prefixed is called a feparatrix.

But if the numerator has not fo many places as the denominator has cyphers, put fo many cyphers before it, viz. at the left hand, as will make up the defect ; fo write Too thus, ,05; and To thus, ,006, &c. And thus

do thefe fractions receive the form of whole numbers. The ift, 2d, 3d, 4th, &c places of decimals counting from the left hand toward the right, are called primes, feconds, thirds, fourths, &c.

We may confider unity as a fixed point from whence whole numbers proceed infinitely increafing toward the left hand, and decimals infinitely decreafing toward the right hand to o, as in the following