From 45 Take 21 24 ΣΤ 24 or the Anfaver. Proof. Add the lefs number and the remainder together, as in whole numbers. Example 2. Subtract from 3 of 4. or, therefore I can take from 24. of is Qu. 3. What is the difference between and 28-Anf. 27701 Qu. 4. What is the difference between 263 and 54%?Anf. 2811. Qu. 5. What is the difference between 14 and of 19? Anf. :7z.. Multiplication of Vulgar Fractions. Rule. Reduce whole and mixed numbers, compound fractions, and fractions of different denominations, to fimple fractions of the fame denomination; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator, and fuch fraction will be the true product required. Example 1. Multiply by 4. Example 2. What is the product of 25 multiplied by %, In this example 2 378 756 7938 is to be reduced to its equivalent fraction, and of must be reduced to its fimple fraction, 8 42 or, then the queftion will be, what is the product of ,, and multiplied together? Q. 3. What is the product of of, by ofAnf. 1% or 78. 120 Qu. 4. What is the product of 24 by?—Anf. 48 or 16. Qu. 5. What is the product of of 7 by 1⁄2?—Ans. 13. 2. 6. 29 T. Thus it may be feen, that multiplication of vulgar fractions is performed in the fame manner as reducing a compound fraction to a fimple one *. Divifion of Vulgar Fractions. Rule. Prepare all the fractions for division in the fame manner as for addition, fubtraction, and multiplication; and invert the two terms of the divifor, placing the denominator at the top and the numerator at the bottom; then pro ceed exactly the fame as in multiplication, viz. multiply the If any number be multiplied by a fraction, the product will be Jefs than the multiplicand, and in proportion as the multiplier is lefs than an unit. numerator numerator of the dividend and that figure that is uppermost in the divifor together for a numerator to the quotient: and multiply the denominator of the dividend and the lower figure of the divifor for the denominator of the quotient. Proof. Multiply the quotient by the divifor, as in whole 'numbers. Example 1. Divide by 3-4)( or 24 Answer. 2. Divide of 7 by 4 of 4. In this example, of 7 is equal to 4, and 3 of 4 is equal toor; therefore I say, divide 14 by -Anf. & or 28. 3. Divide by 3. Anf. 3. # 4. Divide 10 by 1-Anf. 40 or 54. 5. Divide 7 by ofAnf. 405 or 617*. Rule. Prepare the fractions as for the four foregoing rules; and then having placed the three numbers in their proper order according to their proportion, invert the first term or fraction, tranfpofing the numerator and denominator, as in the foregoing rule; then multiply all the three numerators together for a numerator, and all the denominators together for a denominator, and this fraction will be the answer required. Proof The fame as in whole numbers. Example 1. If 3 of an ell English cost of a pound, what will 3 of an ell Flemish coft? In this example I fay, if 3 of 1⁄2 of a yard (which is an ell English) cost of a pound, what will 3 of 2 of a yard (which is an ell Flemish) coft? I then reduce the compound fraction of to a fimple one, and it is or, and alfo the fraction of is of a yard, which is of the fame denomination with the first * If a whole number be divided by a proper fraction, the quotient will be greater than the dividend; but if any fraction be divided by a whole number, the quotient will be lefs than the dividend. VOL. I. Ee number, number, viz. a fraction of a yard; and inverting the firft term the question will ftand thus, coft, The answer or 1s. 114d. 108 1120 3. Then multiplying the three uppermoft figures of the fractions together for a numerator, and the three undermoft figures for a denominator, the answer is which, reduced to its real value, is 15. 118. 108 7120 of a pound, of a penny. Here it must be observed, that the first and third fractions must be reduced to the fame denomination as in whole numbers, as feen in the foregoing example, where they are both fractions of a yard; and the fourth fraction is of the fame denomination with the fecond... Qu. 2. If of a gallon of brandy cost of a pound, what will 123 coft at that, rate?-Anf., or 71. os. 83d. §. Qu. 3. If of a bale of linen coft 14%. 145. what will 10 bales coft at that rate?—Answer 1227, 108. Qu. 4. If 12 lb. of fugar coft 15s. 9d. what is the price of -481lb, ?-Anfwer, 34. os. 9 d. 1. J Rule of Three inverfe in Vulgar Fra&tions. Rule. Prepare all the fractions as for the foregoing rule, * then confider (as, taught in the rule of three in whole num、 bers) whether the quefiion belongs to the inverfe or direct rule, and if it belong to the rule of three inverse, the third fraction is to be inverted, by transpofing the numerator and denominator; and the work is wrought exactly in the fame manner as in the direct rule, by multiplying the three uppermost terms of the fractions together for a numerator, and the undermoft terms of the three fractions for a denominator; -and-the fraction thus formed will be the answer. • Proof. As before in whole numbers. Example. If A lent B4 of 1000l. for 3 of much muft Blend A for of a year in return ? a year, how After After difpofing of the fractions as before directed, I consider that of a year being a longer time than 4, it will not require fo much principal lent, therefore the greater of the first and third numbers must be the divifor (as in whole numbers); the third fraction therefore must be inverted, and the question will stand thus: If of a year Answer 3000, or 158118, equal to 1597. 145. 71⁄23d. Questions both in this rule and the former are proved by back-ftating the queftion, as in whole numbers; thus the foregoing example may be proved by faying, if of 000/. principal require of a year, what will of 1000l. require? and the answer is 230, or of a year. 588 14 189 equal to 24 yards. 2.2. How much fhalloon will it require at of a yard wide to line the garments made with 10 yards of cloth at 1 yard wide?-Anf. 53, or 49, Qu. 3. If 12 men can mow 24 acres in 10 days, how many days will 6 men require to do the fame?-Anfwer 21 days. 2. 4. If a board be of a foot in breadth, how many inches in length will make a fquare foot?—Anf, 16 inches. From what has been delivered in this fection concerning vulgar fractions, it is plain that every other rule in arithmetic may be wrought by vulgar fractions as well as by whole numbers, as the operation in both cafes depends upon the fame principle; thus, in the rule of three direct in vulgar fractions, inverting the first fraction, and multiplying it by the second and third, is the fame as multiplying the second and third fractions together, and dividing by the firft's and in the inverfe rule, inverting the third fraction and multiplying it by the first and fecond, is equal to dividing the product of the first and fecond fractions by the third, as the learner may prove at his leifure. |