Examples. Reduce the following fractions to others equal thereto, which shall have a common denominator. To reduce an improper fraction to a whole or mixed number. Rule. Divide the numerator by the denominator, and the tient is the whole or mixed number required. Examples. 34. Bring to a whole number? 35. 45 Answ. 373 6 36. 25 87 quo 39. 40. 96 Anw. 5. Anw. 107 6 37.444 T 1736 38. T 34 8 5531/ Problem V. To reduce a whole or mixed number to an improper fraction. 1. A Whole Number. 1. Subscribe 1 under the given whole number, for a denominator to express it fraction-wise, 8,; 17, 17. 2. But if it be required to reduce a whole number to a fraction, whose denominator is given: multiply the said whole number by the given denominator, for a numerator to the said denominator. As suppose 7 given to be reduced to a fraction whose denominator shall be 4; now 7 multiplied by 4 makes 28 for the numerator of 23, the fraction required. 28 Examples. 43. Bring 5 to a fraction whose denominator is 197 Answ.. 44. Reduce 3 to a fraction whose denominator is 18? Answ. 144 45. Reduce 6 to a fraction whose denominator is 167 Answ.. II. A mixt Number. Multiply the whole number by the denominator of the annexed fraction, and add the numerator to the product for the numerator of the improper fraction required, and the denominator of the fractional part is the denominator, Application. Let 3 be given to be reduced to an improper fraction, I multiply 3 by 4 and the product is 4 2 32 12, to which adding 2 the numerator of the fractional part, the sum 14 is the numerator of the fraction sought, and 4 the denominator; so then is the improper fraction equal to 32 2. E. I. Answ. Answ. + 4 I Of Compound Fractions. Problem VI. To reduce a compound fraction to a simple fraction. Rule. Multiply the numerators together for a numerator, and the denominators for a denominator. Note. If any denominator of 1 member of a compound fraction be equal to the numerator of another member thereof, these equal numerators and denominators may be erased, and the other members continually multiplied, (as Rule) will produce the fraction required in lower For instance, if it be required to reduce of 3 of to a simple fraction, erasing the equal numerators, they 2 3 4 terms. 43 will stand thus:-of-of-then 2 being the only nume 3 A 5 rator not erased, and 5 the only denominator, the fraction is that required, and equal to the fraction which would be produced by the continual multiplication of the nume rators and denominators: for it is manifest the numerator 2 of the fraction is to be multiplied by 3 and 4, and the denominator 5 by the same, in which case the fraction produced will be equal to the fraction multiplied. Problem VII. To find what fraction of a higher or greater denomina tion, a lesser or divers lesser denominations are. Rule. Reduce the given denominators to the lowest mentioned for a numerator, and unity, of which they are to be the fraction K 3 fraction to the same, for a denominator, and bring the fraction so found to its least terms, 58. 56. What part of a pound is 138. 4d. ? Answ. 64. What part of a b. Troy is 1003. 10dwt. 10gr.? Problem VIII. To find the value of a fraction, viz. Having given a fraction of a greater denomination, to find how many of the lesser are equal thereto. Rule. Multiply the numerator of the given fraction by that number which one of the greater containeth of the lesser, and divide the product by the denominator, and if any thing remain, multiply the remainder by the number which one of the denomination last found the contains of the next lesser, and so proceed till nothing remains, or the lowest lowest be come to, and the several quotients express the denominations equivalent to the fraction given. 7 20 8) 140 Application. Let of a pound be given to find its value; I multiply 7 by 20 the number of shillings in 17. and the product 140 I divide by the denominator 8, and get the quotient 17, the number 17 4 remains. of twentieth parts or shillings; and 4 remaining, I multiply by 12, and again divide the product by 8, find the quotient 6 for pence, and nothing remaining, I bring the quotients together, and thereby find 17s. 6d. the lesser denominations, equal to 12 8) 48 6 To reduce a fraction of a lower denomination to a fraction of a higher. Rule. Make it a compound fraction and reduce it to a simple one. Application. |