EXAMPLES. Reauce 124 guilders, 14 stivers into federal money. Guil. As 1 cts. Guil. $ d. C. m. 39 : : 124,7 : 48, 6 3 3 Ans. mills. G. mills. G. As 390 1 48633: 124,7 Proof. V OF HAMBURGH, IN GERMANY. Accounts are kept in Hamburgh in marks, sous and deniers-lubs, and by some in rix dollars. 12 deniers-lubs make 1 sous-lubs. 3 mark-lubs, NOTE.-A mark is 1 rix-dollar. 33 cts. or just of a dollar RULE. Divide the marks by 3, the quotient will be dollars. EXAMPLES. Reduce 641 marks, 8 sous, to federal money. 3)641,5 $213,833 Ans. But to reduce federal Money into Marks, multiply the giv en sum by 3, &c. EXAMPLES. Reduce 121 dollars, 90 cts. into marks banco. 121,90 3 365,70 365 marks 11 sous, 2,4 den. Ans. VI. OF SPAIN. Accounts are kept in Spain in piastres, rials and marva dies S34 marvadies of plate make 1 rial of plate. 8 rials of plate 1 piastre or piece 01 8. To reduce rials of plate to Federal Money. Since a rial of plate is 10 cents or 1 dime, you need only call the rials so many dimes, and it is done. EXAMPLES. 485 rials=485 dimes48 dols. 50 cts. &c. But to reduce cents into rials of plate, divide by 10Thus, 845 cents÷-10-84,584 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 reas, how many cents? NOTE. When the reas are less than 100, place a cypher before them. Thus, 211,048x124-26169,952 cts, 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 33 milreas, 830 reas. Ans 2. In 24 dols. 92 cents 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. EXAMPLES. 148 194 554 1. In 641 Tales of China, how many cents F Ans. 94868 2. In 50 Pagodas of Inaia, how many cents? Ans. 9700 3. In 98 Rupees of Bengal, How many cents? Ans. 5439 155 VULGAR FRACTIONS. HAVING briefly introduced Vulgar Fractions immediately 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 immediately 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 nu merater is less than the denominator, asif. &c. 2. An Improper Fraction, is when the numerator ex• ceeds the denominator, as Y, &c. 3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, & of 11⁄2 4 of 2 of 2, &c. 4. A Mixed Number, is composed of a whole number and a fraction, thus 81, 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 ke 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 2. Divide the seco lines as before, and so on till there are no two numbs that can be divided; then the Atinued product of the divisors and quotients, will give the multiple required. EXAMPLES. 1. What is the least common multiple of 4, 5, 6 and 10 ? Operation, X5)4 5 6 10 ×2)4 1 6 2 X2 1×3 1 5×2×2×3=60 Ans. 2. What is the least common multiple of 6 and 8. Ans. 24. 2. 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 on, always dividing the last divisor by the last remainder, till nothing remains; the last divisor is the common measuré * 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 he greatest common measure last found be the answer. Or, if you choose, you may take that easy method in 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. Divide the numerator by the denominator, and the quotient will be the value sought. EXAMPLES. 933 1. Find the value of 43 |