15 2. Reduce, 20%, and to a common denominaAns. 68, 60, 60, 60° tor. 8 27 42 16 3. Reduce, and to a common denominator. Case 6. Ans, 30, 30. 81 45 50 1. Reduce, of a penny to the fraction of a pound. 2 of 1 of 20-720-380 Ans. 2. Reduce of a pennyweight to the fraction of a lb. troy. Ans 10 3. Reduce of a nail to the fraction of a yard. Ans. 13 138. 4. Reduce of a pint to the fraction of a hogshead: Ans. 1032 5 of a furlong to the fraction of a mile. Ans. 12. 5. Reduce 1. Reduce 1810 2. Reduce 232 3. Reduce 6 pois. CASE 7. of a dollar to the fraction of a cent. Ans. 4 X 100 1840 400 5 2 of a cwt. to the fraction of lb. avoirdu- 4. Reduce 14 of a yard to the fraction of a nail. CASE 8. 1. Reduce of a dollar to its proper value. 4 100 Ans.. 5)400 Ans. 80 cts. 2. Reduce of a shilling to its proper value. Case 9. 1. Reduce 80 cents to the fraction of a dollar. 2. Reduce 5s. 4d. to the fraction of a pound. 4 Ans. l. 3. Reduce 6 months 2 weeks to the fraction of a year. Ans. year. 4. Reduce 2 quarters 3 nails to the fraction of a yard. Ans. 1 yards. ADDITION OF VULGAR FRACTIONS. Rule. Reduce the fraction to a common denominator, and add the numerators together for a numerator to the common denominator. Note. If a mixed number is given, it is better only to make use of the fractional part in performing the operation, until the fractions are added together, and then add the whole number by simple addition. Note 2.-If fractions be of different denominations, find the proper value of each separately, and add them. together by compound addition. Questions. Repeat the rule for performing addition of vulgar fractions. What is to be noted when a mixed number is given? What is to be noted when different denominations MULTIPLICATION OF VULGAR FRACTIONS. Rule. Multiply all the numerators of the given fraction together for a new numerator, and all the denominators for a new denominator. Note. It will frequently be necessary to prepare the given terms for the operation by the rules of reduction. Questions. Repeat the rule for performing multiplication of vulgar fractions. What is to be noted with respect to the preparation of the given terms? Reduce the given fraction to a common denominator, then subtract the less numerator from the greater, and place the difference over the common denomina tor. But if the lower denominator be greater, subtract it from the common denominator, adding in the upper denominator, and carry one to the units' place of the whole number. Note. When the fractions are of different denominations, reduce them to their proper value, and take their difference by compound subtraction. Questions. How do you perform subtraction of vulgar fractions? What is to be done when the lower numerator is the greater? What is to be noted when the fractions are of different denominations? 1. From take 3. Examples. 5 × 5—25 Reduced to com. den. 25=24—16 Ans. Prepare the fractions if necessary; invert the divisor, and multiply the numerators together for a new numerator, and the denominators for a new denomi Repeat the rule for performing division of vulgar fractions. 1. Prepare the given terms, if preparation be neces sary, by reduction, and state the question as in whole numbers. 2. Then invert the dividing term, and multiply all the numerators together, and all the denominators together for the answer. Questions. If it is found necessary to prepare the given terms previously to stating the question, by what rule is it to be done, and how is the question then to be stated? How do you then proceed to work the question? Examples. 1. If of a yard cost . what will of a yd. cost? 2. When 34 yards cost 93s. what buys 43 yards? 3. How many yards of linen to line 20 yards of baize, that is Ans. 14s. 3d. wide, will be sufficient yards wide? Ans. 12 yards. 4. How much will pay for 4 pieces of cloth, each 273 yards, at 15s. per yard? Ans. 861 19s. 5. What will of a cwt. cost, when 5 cwt. cost 3147? Ans. 21. 7s. 418d. 6. If of a pound of cinnamon bring of a dollar, what will 13 pounds come to? Ans: $2.7418. 7. When 10 men can finish a piece of work in 203 days, in how many days can 6 men do the same? Ans. 344 days. 8. What will of 23 cwt. of chocolate come to, when 6 pounds cost of a dollar? Ans. $10.7635. DECIMAL FRACTIONS. A decimal fraction is a part of a whole number, or unit denoted by a point placed to the left of a figure or figures, as .1.12 .123. I |