29. What principal on interest at 6 per cent per annum, compound interest, for 2 years, will yield $27.81 interest? (See Supplement to Simple Interest, I.) Ans. $225. 30. What principal on interest at 7 per cent per annum, compound interest, for 3 years, will amount to £367 10s. 3.096d.? Ans. £300. 31. A lady read 20 pages in 4 days, 30 pages in 6 days, and 40 pages in 8 days; what was the average number of pages read by her in a day? Ans. 5 pages. 32. The attendance at a certain school for 6 days was as follows: 232, 236, 234, 235, 231, and 236 scholars; what was the average attendance per day? Ans. 234. 33. Mar. 1, 1848. P. H. called to pay the bond I held against him for $1000 dated May 15, 1847, interest at 7 per cent per annum; what amount did he pay me? Ans. $1055.42. 34. If a man's annual income be $1200, how much may he spend in a day to save of his income? Ans. $2.63+ 35. If a bankrupt compound with his creditors for 62 cents on the dollar, how much must A. receive, to whom he owes $400? how much must B. receive, to whom he owes $464? how much for C. to whom he owes $484.64? how much for D. to whom he owes $648.72? how much for E. to whom he owes $912.64 ? Ans {A. 8250; B. $290 C. $302.90; D. $405.45; E. $570.40. ARITHMETIC. PART II. VULGAR FRACTIONS. ALL that should have been said in this place may be found on pages 41 and 42. If the learner has forgotten, or has not learned, the definitions of a Vulgar Fraction, and the different classes of Vulgar Fractions, he should turn over to the place mentioned, and make himself familiar with them, before he begins to work the following rules. I. To find the least common multiple of several numbers; i. e. the least number that may be divided by each of them, and leave no remainder. RULE 1.-Write the given numbers in a line; divide two or more of them, (as many as possible,) by some number that will go into the greatest number of terms without a remainder, and bring the rest down. 2. Divide the quotients, and what you bring down as before; and so continue to do, until there is no number, except unity, that will go into any two of them without a remainder. 3. Multiply what is left with the divisors, for the least common multiple. (See the 1st example.) EXAMPLES. 1. Find the least common multiple of 4, 6, and 8. 44 6 8 | 1 6 2 Ans. 24. 1X3X1 24. or, 4 x 2 x 3 = 24. What is a Vulgar Fraction? a simple fraction? a proper fraction? an improper fraction? a compound fraction? a mixed number? What is meant by the least common multiple of several numbers? What is the rule for finding it-1st? 2d? 3d? 2. Find the least common multiple of 2, 4, 6, 8, and 10. Ans. 120. 3. Find the least common multiple of 3, 5, 6, and 9. Ans. 90. 4. Find the least common multiple of 12, 16, 24, and 48. Ans. 48. 5. Find the least common multiple of 32, 36, 48, and 60. Ans. 1440. 6. Find the least common multiple of the nine digits. Ans. 2520. II. To find the greatest common measure of two or more numbers. RULE 1.-Divide the greater number by the less, and then divide the divisor by the remainder, and so on, till nothing remains; the last divisor will be the greatest com mon measure. 2. When there are more than two terms, take the common measure of two of them, and go through the same process with that and the next, and so on; the last divisor will be the common measure of all the terms. EXAMPLES. 7. Find the greatest common measure of 24 and 60. 8. Find the greatest common measure of 24, 60, and 96. 24)60(2 48 12)24(2 12)96(8 Ans. 12. What is the rule for finding the greatest common measure of two or more terms? 9. Find the greatest common measure of 30, 36, 54, and 72. Ans. 6. 10. Find the greatest common measure of 91, 117, and 130. Ans. 13 REDUCTION OF VULGAR FRACTIONS. REDUCTION of Vulgar Fractions is the method of changing the terms of a fraction into others, retaining the same value. I. To reduce fractions to their lowest terms. RULE. Find the greatest common measure by Case II., and by it, divide both terms of the fraction. II. To reduce a mixed number to an improper fraction. RULE.-Multiply the whole number by the denominator of the fraction, and to the product add the numerator for a new numerator, under which place the denominator in the usual way. What is Reduction of Vulgar Fractions? How do you reduce a fraction to its lowest terms? III. To reduce an improper fraction to a whole or mixed number. RULE.-Divide the numerator by the denominator for the whole number, and place the denominator under the remainder for the fractional part. Ans. 361. Ans. 393. Ans. 683. 26. Reduce 289 to a mixed number. 28. Reduce 3415 to its equivalent number. IV. To reduce a compound fraction to a simple fraction. RULE 1.-Reduce whole and mixed numbers into simple fractions. 2.-Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; or cancel as in Ex. 30. 30. Reduce of of of to a simple fraction. Ans.. Ans. Ans. 3. 31. Reduce of of 1 to a simple fraction. What is the rule for reducing a mixed number into an improper fraction? for bringing an improper fraction into a whole or mixed number? How do you reduce a compound fraction to a simple one-1st? 2d? |