But to recluce cents into rials of plate, divide by 10. Thus, 845 cents:-10=84,5=84 rials, 17 inarvadies, &ck VII. OF PORTUGAL. Accounts are kept throughout this kingdom in milreas, and reas, reckoning 1000 reas to a milrea. No'r E.A mjirea 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 5-10 milias how inany cents ? 549x1212100 cents,=8101, 60cts. Ans. 2. in 21! mireas, & reas, how many cents : Nont.--cn the reas are less than 100, place a cy. pher before them.Thus, 211,048x124=26169,952 cts. or 261 dols. 69 cents, 9 mills. + Ans. But to reruce cents into milreas, divide them by 124; and if deciinals 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 ? 4193-124=33,830+ or 63milr. 830reas. Ains. 2. In 24 dols. 92 cts. how many milocus of Portugal ? Ans. 20 milieas, 096 reas. 194 55) XXXMILES. 1. In 641 Tales of China, bow many cents ? Ans. 94868 2. In 50 Pagodas India, how many cents ? Ans. 9700 3. In 98 Rupees of Bengal, low many cents ? Ans, 5499 8 7 1 2 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 nuinerator is less than the denominator, as ; it , &c. 2. An Improper Fraction, is when the numerator exceeds the denominator, as $ } *, &c. 3. A Compound Fraciion, is the fraction of a fraction, coupled by the word of, thus, of in, 1 of of i, &c. 4. A Hired Number, is composed of a whole number and a fraction, thus, 81, 141, &c. 5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, š=>, and 12 thus, '*, &c. &c 6. The common mersure of two or inore numbers, is that number which will divide each of them without a renainder; thus, 3 is the common measure of 12, 24 and 50; 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 diuinbers, 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 cominon multiple of two or more numbers. RULL. i. Diviile by any number that will divide two or more of the given numbers without a remainder, and set the quotients, together with the utrdivided numbers, in a line beneatit. 2. Divide the second lines as ivefore, ami so 031 Here are no two cubers tint can be divided ; th continued product of the divisors and quotients, will give the multiple required. 1. What is the least common multiple of 4, 5, 6 and 107 Operation, X5)4 5 6 10 EXAMPLES. a 5 X 2 X 2 XS=60 Ans. 2. What is the least common multiple of 6 and 8? Ans. 24 5. 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 coinmon measure, and the quotients will make the fraction required. *To find the greatest common measure of nore 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 ell the numbers to the last; then will the greatest COMTEOR ELCASUT? lost format de the writer, * OrgIf you choose, you may take that easy method in OR EXAMPLES, 48 종응 36 47 13 fins. 196 1. Reduce to its lowest terms. 8)$#(1 Operation. 0848 common mea. 8). Ans. Rem. 2. Reduce to its lowest terms. ins. 24 3. Reduce 182 to its lowest terms. 4. Reduce 3798 to its lowest terms. Ans. CASE II. To reduce a mixed number to its equivalent improper fi'action. RULE. 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. Ans. ** 18 100 1. Reduce 45% to its equivalent improper fraction. 45x8+7=397 Ans. 2. Reduce 1943 to its equivalent improper fraction. 3. Reduce 16106 to an improper fraction. Ans. 4618 4. Reduce 616 to its equivalent improper fraction. Ans. 22085 RULE. Divide the numerator by the denominator, and the quotient will be the value sought. CASE IV. a denominator. RULE. Multiply the whole number by the given denominado place the product over the said denominator, and its form the traction required. EXASIPLES. 1. Reduce 7 to a fraction whose denominator ti 9. Thus, 7x9=65, and 0,3 the ciste 2. Reduce 18 to a fraction whose denominat 1 be 12. Hirs. 3. Reduce 100 to its equivalent fraction, baring for a denominator. ins. 9000 CASE V. To reduce a compound fraction to a simple 01:e cene value. KULE, 1. Reduce all whole and mixeil numbers, to therani valent fractions.' 2. Multiply all the numerators together for a man? merator, and all the denoninators for a new design tor; and they will form the fraction required. 900 EXAMPLES. 1. Reduce i of ļof of to a simple question 1 X2 X3 X4 ਹ ਸ 2XS,X4X10 2. Reduce of of Ito a single fractim. Ans. 3. Reduce of 1 of to a single fraction. Ans. 934 1562 4. Reduce j of, of 8 to il simple fraction. Ans. 5. Reduce of 2) to a simple fraction. atins, 12 660 120 NOTE.-If the denominator of any member of bound fraction be equal to the numero fui of |