Or, if you choose, you may take that easy method in Problem I. (page 09.) RULE.-Multiply the whole number by the denominator of the gi "En fraction, and to the product add the numerator, this sum written Love the denominator will form the fraction required To find the value of an improper fraction. RTL.E.-Divide the numerator by the denominator, and the quo CASE IV. To reduce a whole number to an equivalent fraction, hav ing a given denominator. RULE.-Multiply the whole number by the given denominator place the product over the said denominator, and it will form the fraction required. 12. EXAMPLES. 1. Reduce 7 to a fraction whose denominator will be 9. Thus, 7×9=63, and 43 the Ans. 2. Reduce 18 to a fraction whose denominator shall be Ans. 21 3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 8° 8° =1o CASE V. To reduce a compound fraction to a simple one of equa' value. RULE.-1. Reduce all whole and mixed numbers to their equiva lent fractions. 2. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required. EXAMPLES. 1. Reduce of of of to a simple fraction 1×2×3×4 ==% Ans. Ans, & 2×3×4×10 2. Reduce of 4 of 3 to a single fraction. 4. Reduce of 3 of 8 to a simple fraction. Ans. 1 Ans. 12=31 5. Reduce of 1 of 42 to a simple fraction. Ans. 188217% -If the denominator of any member of a com action be equal to the numerator of another mem ver thereof, they may both be expunged, and the other members continually multiplied (as by the rule) will produce the fraction required in lower terms. 6. Reduce of 3 of to a simple fraction. 7. Reduce of of 1⁄2 of 1 to a simple fraction. CASE VI. Ans. fo reduce fractions of different denominations to equiva lent fractions having a common denominator. RULE I. 1. Reduce all fractions to simple terms. 2. Multiply each numerator into all the denominators except its own, for a new numerator; and all the denominators into each other continually for a common denominator; this written under the sevecal new numerators will give the fractions required. EXAMPLES. 1. Reduce, 3, 3, to equivalent fractions, having a comnon denominator. ÷ + 3 + ?=24 common denominator. 24 24 24 denominators. !. Reduce 7, f, and, to a common denominator. Ans. 84, 84, and $88. §. Reduce 1, §, §, and 7, to a common denominator. 192 Ans. 14, 1, 18, and fit 2881 2881 4. Reduce,2%, and, to a common denominator = 300 400 800 -and 1000 1000 1000 ==% 1% and 11 Ans. 8 5. Reduce 3,, and 121, to a common denominator. Ans.,,. 6. Reduce 3, 3, and 1⁄2 of 11, to a common denominator 768 34561 3456 3456° The foregoing is a general rule for reducing fractions to a common denominator; but as it will save much labour to keep the fractions in the lowest terms possible, the following Rule is much preferable. RULE II. For reducing fractions to the least common denominator. (By Rule, page 143) find the least common multiple of all the denominators of the given fractions, and it will be the common denominator required, in which divide each particular denominator, and multiply the quotient by its own numerator, for a new numerator, and the new numo rators being placed over the common denominator, will ex press the fractions required in their lowest terns. EXAMPLES. 1. Reduce 1⁄2, 1, and §, to their least common deromirato 4)2 1 8 2)2 1 2 1 1 1 4x2=8 the least com. denominator. 8 2×1-4 the 1st numerator. 8÷8×5=5 the 3d numerator. These numbers placed over the denominator, give the answer,,, equal in value, and in much lower terms than the general Rule would produce 2. Reduce,, and, to their least common denomina tor. Ans. 47, 41, 42. 3 Reduce and to their least common denomi nat Ans. 1 4. Reduce and to their least common denominator. Ans. 1 1 1 CASE VII. To Reduce the fraction of one denomination to the fraction of another, retaining the same value. RULE. Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing t with all the denominations between it and that denomination you would reduce it to; lastly, reduce this com Found fraction to a single one, by Case V. EXAMPLES. 1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes 5 X 1 X 1 6 × 12 × 20 14 0 of 11⁄2 of 3% of a pound. Ans. 1440 2. Reduce of a pound to the fraction of a penny. Compared thus 1 of 2 of d. 3. Reduce 1⁄2 of a farthing to the fraction of a snilling. 124 Ans. 4. Reduce of a shilling to the fraction of a pouna. 5. Reduce of a pwt. to the fraction of a pound troy. Ans. T 6. Reduce of a pound avoirdupois to the fraction of cwt. ៖ Ans. (cot. 126 7. What part of a pound avoirdupois is of a cut. Compounded thus 1 of 1 of 2011;=f Ans. 28 8. What part of an hour is of a week. Ans |