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 milrcas, 48 reas, how many cents? NOTE. When the reas are less than 100, place a cypher before them. Thus, 211,048 × 124=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 fai as three decimal places; then the whole numbers thereo. 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. Pagodas of India, Rupee of Bengal. EXAMPLES. 1. In 641 Tales of China, how many cents? 148 194 55 Ans. 94868 2. In 50 Pagodas of India, how many cents? Ans. 9700 3. In 98 Rupees of Bengal how many cents? Ans. 5439 VULGAR FRACTIONS. HAVING briefly introduced Vulgar Fractions immediately after reduction of whole numbers, and given some general definitions, and a few such problems there in 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 numerator is less than the denominator, as 18, &c. 2. An Improper Fraction, is when the numerator ex ceeds the denominator, as 7, 7 12. &c. 3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, of of, &c. 4. A Mixed Number, is composed of a whole number and a fraction, thus 83, 142, &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 2 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. i. 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 the continued product of the divisors and quotients, will give the multiple required. EXAMPLES. 1. What is the least common multiple of 4, 5, 6 & 10? Operation, X5)4 5 5 6 10 X2)4 1 6 2 X2 1 X3 1 5X2 X2 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 on, always dividing the last divisor by the last remainder, till nothing remains; the last divisor is the common measure.* 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 la. found be the answer ŐR, if you choose, 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 #equired. EXAMPLES. 1. Reduce 45% to its equivalent improper fraction. 45x8+7=307 Ans. 2. Reduce 19 to its equivalent improper fraction. Ans. 354 18 Divide the numerator by the denominator, and the quotient. will be the value sought. 24 CASE IV. To reduce a whole number to an equvalent 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. EXAMPLES. 1. Reduce 7 to a fraction whose denominator will be 9. Thus, 7X9-63, and 3 the Ans. 2. Reduce 18 to a fraction whose denominator shall Ans. 216 be 12. 12 3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 90000 100 CASE V. 60 To reduce a compound fraction to a simple one of equal value. RULE. 1. Reduce all whole and mixed numbers to their equi valent 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. 4 1. Reduce of of of to a simple question. 18 1X2X8X4 2×3×4x10 24 10 Ans. 2. Reduce of of 3 to a single fraction. Ans. 3. Reduce of 1 of 1 to a single fraction. 45 Ans. 336 4. Reduce of 5 of 8 to a simple fraction. 1300 Ans. 120=31 5. Reduce of 42 to a simple fraction. Ans. 18-211 12660 NOTE. If the denominator of any member of a com pound fraction be equal to the numerator of another mem |