Rule. Multiply the numerators together for a new numerator, and the denominators for a new denominator, which reduce, if necessary, to their lowest terms. Case 5. To find a common denominator. Rule. 1. Find the least common denominator, by dividing the given denominators by any number that will divide two or more without a remainder. 2. Set the quotients and individual numbers underneath, and continue the division till no two numbers can be lessened. 3. Multiply the quotients and the divisor or divisors, and the product will be the least common denominator; into which, divide each denominator, and multiply the quotient by its own numerator for a new numerator; and place the new numerator over the denominator, and the fractions are expressed in their lowest terms. Case 6. To reduce fractions of one denomination to fractions of a greater denomination, but retaining the same value. Reduce the given fraction to a compound fraction, by multiplying it with all the denominations between the given fraction and the one to which it is to be reduced; which reduce to a single fraction. Case 7. To reduce the fraction of one denomination to the fraction of another less denomination, but retaining the same value. Rule. Multiply the numerator by the parts of the denominator between the given fraction and that to which it is to be reduced, and place the product for a new numerator over the given denominator, which reduce to its lowest terms. Case 8. To reduce a fraction to its proper value. Rule. Multiply the numerator by the next lowest denomination, and divide by the denominator. of Case 9. To reduce any given value or quantity to the fraction any greater denomination. Rule. Reduce the given sum to the lowest denomination mentioned for a numerator, and the denomination of which you wish to make it a fraction, to the same name, for a denominator. Questions. Repeat the rule for reducing fractions to their lowest terms. When it is required to reduce a mixed number to an improper fraction, how do you proceed? When it is required to reduce an improper fraction to a mixed number, how is the operation performed? Repeat the rule for reducing a compound fraction to a single one. When you wish to find a common denominator, what is first to be done? What is to be done in the second place? What is to be done to complete the operation of finding a common denominator? Repeat the rule by which you reduce fractions of one denomination to fractions of another denomination, but retaining the same value. How do you reduce a fraction of one denomination to a fraction of a less denomination, but retaining the same value? How do you reduce a fraction to its proper value? By what rule do you reduce any given value or quantity to the fraction of any greater value or quantity? 1. Reduce 36 to an improper fraction. 2. Reduce 45 to an improper fraction. 1. Reduce of 3 of 3 of to a single fraction. 1X2X3X4 24 2) ==}: Or, 1 of 3 of 3 of 4-2=}. 2X3X4X5=120° 2. Reduce of of 11 of 13 to a single fraction. 3. Reduce of 15 of Ans. 572 1071 of to a single fraction. Ans. 420 2717 Case 5. 1. Reduce 2 3)2 3 6 18 2)2 12 ,,, and to a common denominator. 6 1 11 3 3X2X3=18 common denom. 2=9X 19 3=6X 2-12 new nu6 3X 5=15 merat. 18=1X17=17) 2. Reduce, and, to a common denomina tor. Ans. 48 27 42 16 60 80 60 80° 3. Reduce, and 5, to a common denominator. Case 6. Ans. 30, 30, 30 81 45 50 1. Reduce of a penny to the fraction of a pound. of of 0=386£., Ans. 2. Reduce of a pennyweight to the fraction of a lb. troy. Ans. lb. 3. Reduce of a nail to the fraction of a yard. Åns. yd. 4. Reduce of a pint to the fraction of a hogshead. 1. Reduce 1 2. Reduce dupois. Case 7. Ans.hhd. of a dollar to the fraction of a cent. Ans. 4x100 4003ct. 1840 of a cwt. to the fraction of a lb. avoirAns. lb. 3. Reduce of a pound to the fraction of a penny. Case 8. 1. Reduce of a dollar to its proper value. Here: 4x100-5-80cts. Ans. 2. Reduce of a shilling to its proper value. Ans. Ed. Ans. 101d. of a day to its proper quantity. 3. Reduce Ans. 6 hours. 4. Reduce of an acre to its proper quantity. Case 9. Ans. 1R. 10P. 1. Reduce 80 cents to the fraction of a dollar. In a dollarcts.. Ans. 2. Reduce 58. 4d. to the fraction of a pound. Ans. £. 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. yard. 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. Note 3.-When all the denominators are alike, add all the numerators together, and place one of the denominators under the amount. Questions. Repeat the rule for performing addition of vulgar frac tions. What is to be noted, when a mixed number is given? • What is to be noted, when different denominations are given? What is to be noted, when all the denominators are alike? Examples. |