But to reduce cents into rials of plate, divide by 10Thus, 845 cents-10-84,5-84 rials, 17 marvadies, &c. VII. OF PORTUGAL. Accounts are kept throughout this kingdom in milreas, and reas, reckoning 1000 reas to a milrea. NOTE. A milrea is =124 cents; therefore to reduce milreas into Federal Money, multiply by 124, and the product will be cents, and decimals of a cent. EXAMPLES, 1. In 340 milreas how many cents? 340×124-42160 cents,=$421, 60cts. Ans. 2. In 211 milreas, 48 rcas, how many cents? NOTE. When the reas are less than 100, place a cypher before them.-Thus 211,048×12426169,952cts. or 261 dols. 69 cts. 9 mills. + Ans. But to reduce cents into milreas, divide them by 124; and if decimals arise you must carry on the quotient as far as three decimal places; then the whole numbers thereof will be the milreas, and the decimals will be the reas. EXAMPLES. 1. In 4195 cents, how many milreas? 4195-124-33,830+or 53 milreas, 330 reas. Ans. 2. In 24 dols. 92 cts. how many milreas of Portugal ? Ans. 20 milreas, 096 reas. VIII. EAST-INDIA MONEY. To reduce India Money to Federal, viz. Tales of China, multiply with Pagodas of India, Rupee of Bengal, EXAMBLES. 148 194 551 1. In 641 Tales of China, how many cents? 2. In 50 Pagodas of India, how many cents? 3. In 98 Rupees of Bengal, how many cents? Ans. 5439, Ans, 9700, VULGAR FRACTIONS. HAVING briefly introduced Vulgar Fractions imme. diately after reduction of whole numbers, and given some general definitions, and a few such problems therein as were necessary to prepare and lead the scholar immedi ately to decimals; the learner is therefore requested to read those general definitions in page 74. Vulgar Fractions are either proper, improper, single, compound, or mixed. 1. A single, simple, or proper fraction, is when the numerator is less than the denominator, as 2 18, &c. 2. An Improper Fraction, is when the numerator exceeds the denominator, as, &c. 5. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, of, of of, &c. 4. A Mixed Number, is composed of a whole number and a fraction, thus, 8, 14, &c. 5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 8, and 12 thus, 12, &c. 6. The common measure of two or more numbers, is that number which will divide each of them without a remainder; thus, 3 is the common measure of 12, 24 and 30; and the greatest number which will do this, is called the greatest common measure. 7. A number, which can be measured by two or more numbers, is called their common multiple: and if it be the least number that can be so measured, it is called the least common multiple: thus, 24 is the common multiple of 2, 3 and 4; but their least common multiple is 12. To find the least common multiple of two or more numbers. RULE. 1. Divide by any number that will divide two or more of the given numbers without a remainder, and set the quotients, together with the undivided numbers, in a line beneath. 2. Divide the second lines as before, and so on till there are no two numbers that can be divided; then th continued product of the divisors and quotients, will give the multiple required. EXAMPLES. 1. What is the least common multiple of 4, 5, 6 and 107 Operation, X5)4 5 6 10 X2)4 1 6 X2 1X3 1 5x2x2 x3=60 Ans. 2. What is the least common multiple of 6 and 8 ? Ans. 24. 3. What is the least number that 3, 5, 8 and 12 will measure? Ans. 120. 4. What is the least number that can be divided by the 9 digits separately, without a remainder ? Ans. 2520. REDUCTION OF VULGAR FRACTIONS, IS the bringing them out of one form into another, in order to prepare them for the operation of Addition, Subtraction, &c. CASE I. To abbreviate or reduce fractions to their lowest terms. RULE. 1. Find a common measure, by dividing the greater term by the less, and this divisor by the remainder, and so ou, always dividing the last divisor by the last remainder, till nothing remains; the last divisor is the common 2. Divide both of the terms of the fraction by the common measure, and the quotients will make the fraction required. *To find the greatest common measure of more than two numbers, you must find the greatest common measure of two of them as per rule above: then, of that common measure and one of the other numbers, and so on through all the numbers to the last, then will the greatest common measure ast found be the answer OR, If you chuse, you may take that easy method in Problem I. (page 74.) Multiply the whole number by the denominator of the given fraction, and to the product add the numerator, this sum written above the denominator will form the fraction required. EXAMPLES. 1. Reduce 45 to its equivalent improper fraction. 2. Reduce 1913 to its equivalent improper fraction. 45x8+7=367 Ans. Ans. 354 18 3. Reduce 16,1 to an improper fraction. 18 10 100 4. Reduce 611 to its equivalent improper fraction. CASE III. To find the value of an improper fraction. RULE. Divide the numerator by the denominator, and the quotient will be the value sought. Ans. 84 Ans. 8 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 shall be 9. Thus, 7x9=63, and 63 the Ans. 2. Reduce 18 to a fraction whose denominator shall be 12 Ans. 216 s. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 9300-900=100 CASE V. To reduce a compound fraction to a simple one of equal 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 2. Reduce of of to a single fraction. Ans. 3. Reduce of 1 of 1 to a single fraction. 4. Reduce of of 8 to a simple fraction. 288 ins. 836 1500 5. Reduce of 13 423 to a simple fraction. Ans. 12660 36 NOTE. If the denominator of any member of a case pound fraction be equal to the numerator of another mom' |