TROY WEIGHT. 2 From Take 14 5 14 18 Take 14 lbs. ozs. dwts. grs. 7 3 14 11 3 7 15 20 APOTHECARIES WEIGHT. lbs. ozs. drs. scr”. grs. lbs. ozs. drs. scr. grs. From 12 10 5 2 18 From 8 4 6 2 16 Take 6 9 6 2 Take 4 8 7 1 19 18 LIQUID MEASURE. tuns. hhds. gals. qts. pt. hhds. gals. qts. pt. 18 2 52 2 1 From 6 42 3 1 12 3 58 3 0 Take 3 33 3 1 From Take secs. MOTION OR CIRCLE MEASURE. sign, dgs. mins. secs. degs. ms. From 3 8 22 35 From 37 33 35 Take 1 5 37 42 Take 22 35 55 DIVISION OF COMPOUND NUMBERS. A compound number may be divided by a simple number, by regarding each of the terms of the former, as forming a distinct dividend. RULE. Divide the highest term of the compound number by the given divisor, reduce the remainder, (if any) to the next lower denomination, adding it to the number of this denomination, and divide the sum by the divisor, reducing the remainder as before, and proceed, in this way through all the denominations to the last. TROY WEIGHT. 67 5 16 22 by 2. Dividing by 2 is taking 3)33 8 18 11 Here 33 is the quotient, and 1 of a remainder, which is 1 lb. this reduced to the next lower denomination which is ounces, we get 12 + 5 17 ounces, this divided by 2, gives 8 in the quotient, and 1 of a remainder, which is 1 oz., this reduced to the next lower, which is pennyweights, and we get 20 +16=36 pennyweights; 36 divided by 2 gives 18, and no remainder; the next lower denomination is 22 grains, and this also divided by 2 gives 11. All other compound quantities are divided upon the same principle. LAND MEASURE. acs. rds. pr. acs. rds. pr. Divide 45 . 3 32 by 8? Divide 24 3 05 by 5? CLOTH MEASURE. yds. qrs. Rs. Divide 196 2 2 by 4? Divide 48 3 yds. qrs. ns. 3 by 6? AVOIRDUPOIS WEIGHT. tons, cwt. qrs. lbs. tons, cwt. qrs. lbs. Divide 6 14 2 18 by 4? Divide 8 12 3 24 by 8? LIQUID MEASTRE. tuns, hhds.gals. qts. tuns, hhds. gals. qts. Divide 6 4 44 3 by 3? Divide 0 36 62 2 by 4? DRY MEASURE. bush. pks. qts. bush. pks. qts. 64 2 6 by 4.? Divide 84 3 7 by 6? Divide MOTION OR CIRCLE MEASURE. The moon revolves through 12 signs of the Zodiac in 27 days, 7 hours, 42 minutes, 48 seconds. In what time does it describe one sign? Ans. 2d. 6h. 38m. 34s. LECTURE VIII. FRACTIONS SIMPLIFIED. DEFINITIONS, Q. What is a fraction? A. A fraction is an expression of a part, or some parts of any thing considered as a whole. Q. How is it denoted? A. By two numbers, one placed below the other, with a line between them as å, written three-fourths. Q. What is the number above the line called? A. It is called a numerator, (as before mentioned) from the French, numerateur, which determines the number of parts, it also represents a remainder after division. Q. What is the number below the line called? A. It is called a denominator, from the Latin, denomino, because it denominates the number of parts. Q. What are the numerator and denominator considered? A. They are generally considered the terms of a fraction? Q. How are fractions arranged? A. Into four classes, viz: proper, improper, compound, and mixed. Q. What is a proper fraction? A. It is that, whose numerator is less than the denominator, as į or to, &c. Q. What is a complex fraction? A. It is that, which has a fraction in its numerator or denominator, or in both of them: thus, 51, 8, 41. Q. What is an improper fraction? A. It is that whose numerator is greater than the denominator, as or 1, &c. Q. What is a compound fraction? A. It is the fraction of a fraction, or several fractions connected by the proposition of between them, as the and of 4 of a dollar. Q. What is meant by a mixed number? A. A whole number, and a fraction together, as 3}, or 12, &c. Q. Can a whole, or integer number be expressed like a fraction? A. Yes, by writing 1 below it as a denominator, as 3 is i, 4 is 1 or 25 is 2. This is evident, because a unit is neither a multiplier or a divisor, that is, you neither increase or decrease the value of any thing by multiplying or dividing by 1, as 6 x1 = 6, f = 6. Q. How is the value of an improper fraction obtained? A. By dividing the numerator by the denominator, as 3, Q. What is a reciprocal fraction? A. It is a fraction inverted, as is the reciprocal of *. RULES. 1. When the numerator is less than the denominator, the fraction is less than 1, as į or ģ, &c. 2. When the numerator is equal to it, the fraction is equal to 1, asor, &c. 3. When the numerator is greater than the denominator, the fraction is greater than 1, as for f, &c. Q. Can you tell by inspection when a proper fraction may be less than another, as Å, }, ; or 3? A. Certainly, šis greater than }, because the numerator does not shew a division of so many parts, for according to the meaning attached to the words numerator and denominator, it is plain, that a fraction is increased by |