An improper fraction is that of which the numerator is equal to, or greater than the denominator; as, &c. ,, A compound fraction is a fraction of a fraction; as of, or off of 1s, &c. A mixed number consists of a whole number and a fraction; as 44, 73, &c. REDUCTION OF VULGAR FRACTIONS. CASE 1. To reduce a fraction to its lowest terms. RULE. Divide the greater term by the less, and that divisor by the remainder, till nothing be left; the last divisor will be the common measure. Divide both terms by the common measure, and the quotients will be the numerator and denominator of the fraction required: or, Divide the terms by any number that will divide them both without a remainder, and divide the quotients in the same manner, and so on, till no number greater than 1 will divide them; the fraction is then at its lowest terms. Note. If the common measure be 1, the fraction is already at its lowest terms. Ciphers on the right hand of both terms may be rejected; thus #88=4. CASE 2. To reduce several fractions to others, of the same value, and having a common denominator. RULE. Multiply each numerator into all the denominators but its own, for its respective numerator; and all the denominators into each other, for a common denomi nator. 4×5×6=120 Common denominator. 96 Result 1, 1, and 128. 90 120 2. Reduce, 4, and to a common denominator. Result 32, 48 40 to a common denominator. Result 144, 192 240 252. 2889 288 288 288. 4. Reduce,,, and, to a common denominator. 504 40, 840 720. Result 78, 735 560 5. Reduce,,, and to a common denominator. Result 192, 120 200. 60 CASE 3. 2409 240 2409 240 To reduce a mixed number to an improper fraction. RULE. Multiply the whole number by the denominator of the fraction, and add the numerator to the product for a new numerator, under which place the given denomi nator. 1 EXAMPLES. 1. Reduce 12 to an improper fraction. Result 142. 2. Reduce 191 to an improper fraction. Result 3. Reduce 124 to an improper fraction. Result. -4. Reduce 100 to an improper fraction. Result 59. To reduce an improper fraction to a whole or mixed number. RULE. Divide the upper term by the lower. Note. This case and case 3 prove each other. To reduce a compound fraction to a single one. RULE. Multiply the numerators together for a new numerator, and all the denominators for a new denominator. Note. Like figures in the numerators and denominators may be cancelled, and frequently others contracted, by taking their aliquot parts. EXAMPLES. 1. Reduce of of to a single fraction. Result . 3. Reduce of & off to a single fraction. 4. Reduce of of to a single fraction. Result Result. 5. Reduce of of to a single fraction. Result. 4872232 6. Reduce of of to a single fraction. CASE 6. Result f 168 5 To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value. RULE. Make the fraction a compound one, by comparing it with all the denominations between it and that to which it is to be reduced; which fraction reduce to a single one. EXAMPLES. of a penny to the fraction of a pound. of 2018 of a pound. 2. Reduce of a penny to the fraction of a pound. Result L. 3. Reduce of a farthing to the fraction of a shilling. Results. 4. Reduce of a cent to the fraction of a dollar. Result 1dol. 5. Reduce of an oz. troy, to the fraction of a pound. Result lb. 6. Reduce & of a lb. avoirdupois, to the fraction of a cwt. Result cwt. 7. Reduce of pint of wine to the fraction of hhd. 8. Reduce of a minute to the fraction of a day. a CASE 7. Resulthhd. Result day. a To reduce the fraction of one denomination to the fraction of another, but less, retaining the same value. RULE. Multiply the given numerator by the parts of the denomination between it and that to which it is to be reduced, for a new numerator, and place it over the given denominator; which reduce to its lowest terms. Note. This case and case 6 prove each other. 5 EXAMPLE. 1. Reduce 1440 of a pound to the fraction of a penny. 5×20×12-1200-d. Result. 1440 4 2. Reduce 분양이 of a pound to the fraction of a penny. Result d. 3. Reduce of a shilling to the fraction of a farthing. Result qr. 4. Reduce 많이 of a dollar to the fraction of a cent. Result ct. 5. Reduce of a lb. troy, to the fraction of an oz. Result oz. 6. Reduce of a cwt. to the fraction of a lb. avoir dupois. Result lb. 7. Reduce of a hhd. to the fraction of a pint. Result pt. 8 Reduce of a day to the fraction of a minute. Result CASE 8. To reduce a fraction to its proper value or quantity in integers. RULE. Multiply the numerator by the known parts of the integer, and divide by the denominator. J |