4. Reduce 70%. 4pwt. to the fraction of a ft Troy. 5. Anf.tb. Reduce 2qrs. 23”. to the fraction of a yard. 6. Reduce 18s. to the fraction of a guinea. Anf. yd. Anf. G. 7. Reduce 5s. 74d. to the fraction of a dollar. 8. Reduce 215. 7 d. to the fraction of a Anf. dol. moidore. Anf. 3moid. ADDITION of VULGAR FRACTIONS. RULE. Reduce compound fractions to fingle ones; mixed numbers to improper fractions; fractions of different integers to those 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, and 7 together. Or thus, 2184+75+1960. 2. What 2. What is the fum of 6 of 4, 4 of 4 and 91 ? 3. Add .. and d. together. Anf. 128. Anf. 25. 8d. 4. Add of a week, of a day, of an hour, and 444 of a minute together. 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, fubtract the numera tor 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 fubtrahend. EXAMPLE. From 19 take 12719-127=6. 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 denomingtor of another, their equal numerators and denominators may be omitted. I. EXAMPLES. Σ 1. What is the continued product of 4,, of, and 6? DIVISION of VULGAR FRACTIONS. RULE.* Prepare the fractions as before: Then, invert the divifor and proceed exactly as in Multiplication: The products will be the quotient required. DECIMAL FRACTIONS. Decimal Fractions are of such a nature, that 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 fuppofed to be reducible to another, whofe denominator fhall be 10, 100, 1000, &c. viz. Unity, with a number of cyphers annexed; and Fractions with such denominators, are call55 675 &c. ed Decimal Fractions: Such are, TOS TOO210009 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 1000, &c. the denominators need not be expreffed: For the numerator only may be made to exprefs the true value: For this purpose it is only required to write the numerator with a point before it at the left hand, to distinguish it from a whole number, when it confifts of fo many figures as the denominator hath cyphers annexed to unity, or I: So is written,5; 33 ; Tooo 735, &c. 735 ΤΟ Note. The point prefixed is called a Separatrix. 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 5 thus, ,05; and thus, ,006, &c. And thus do these fractions receive the form of whole numbers. The 1ft, 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 TABLE. C Millions ∞X Millions → Millions C Thousands X Thousands Hundredth Parts X Thoufandth Parts w Hundreds ~ Tenth Parts ~ Tens Units From |