What is to be done when the lower numerator is the greater? What is to be noted when the fractions are of dif ferent denominations? 1. From take 3. Examples. 5X5-25 Reduced to com. den. 25-24-1 Ans. Prepare the fractions if necessary; invert the divisor, and multiply the numerators together for a new numerator, and the denominators for a new denomi nator. Question. Repeat the rule for performing division of vulgar fractions. 1. Prepare the given terms, if preparation be neces sary, by reduction, and state the question as in whole numbers. 2. Then invert the dividing term, and multiply all the numerators together, and all the denominators together for the answer. Questions. If it is found necessary to prepare the given terms previously to stating the question, by what rule is it to be done, and how is the question then to be stated? How do you then proceed to work the question? Examples. 1. If of a yard cost 2. what will of a yd. cost? 1x9x5 2. When 31 yards cost 93s. what buys 43 yards? Ans. 14s. 3d. 3. How many yards of linen & wide, will be sufficient to line 20 yards of baize, that is yards wide? Ans. 12 yards. 4. How much will pay for 4 pieces of cloth, each 273 yards, at 153s. per yard? Ans. 861 19s. 5. What will of a cwt. cost, when 53 cwt. cost 311? Ans. 21. 78. 418d. 6. If of a pound of cinnamon bring of a dollar, what will 13 pounds come to? Ans: $2.7418. 7. When 10 men can finish a piece of work in 20 days, in how many days can 6 men do the same? Ans. 34 days. 8. What will of 23 cwt. of chocolate come to, when 6 pounds cost of a dollar? Ans. $10.7635. DECIMAL FRACTIONS. A decimal fraction is a part of a whole number, or unit denoted by a point placed to the left of a figure or figures, as .1.12 .123. The first figure after the point denotes so many tenths of a unit, the second so many hundredths, the third so many thousands, and so on. Decimal fractions are read in the same manner as vulgar fractions: .1 is equal to and reads, .12 1, .123 123 1000 12 A number consisting partly of whole numbers and partly of decimal fractions, is called a mixed number; as, 1.1, 12.12, 123.123. It has already been understood that whole numbers, counting from the right towards the left, increase in a tenfold proportion; but decimals, on the contrary, counting from the left towards the right, decrease in a tenfold proportion; as will be better exemplified in the following table: TABLE. Whole numbers. Tens. Units. 100 of Thousands. Thousands. 10 of Thousands. Thousandth part. 100 Thous. part. 1000 Millth. part. Millions. 100 of Millions. 10 of Millions. Note.-Ciphers placed after decimal figures, neither increase or decrease their value; thus .1, .10, and .100 all express the same value, namely. But ciphers. placed between the decimal point and any other figure, decrease their value in a tenfold proportion; as .1, .01, .001; and they all express different values, namely, o, 0, 1000. Questions. What are decimal fractions, and how are they denoted? How are decimal fractions to be read? What is a number called, which consists partly of a whole number and partly of a decimal ? In what manner do whole numbers increase, and in what manner do decimals decrease in value? What do you observe by the inspection of the table? What is to be noted with respect to placing ciphers after decimal figures? What is to be noted with respect to placing ciphers between the decimal point and any other figure? ADDITION OF DECIMALS. Rule. Set down the given numbers under each other; observing to place tenths under tenths, hundredths under hundredths, &c.; and perform the operation in the same manner as addition of whole numbers. Note that all the decimal points stand exactly under each other, and that the decimal point in the product stands exactly under those in the example. Questions. How are decimal numbers, given to be added, to be set down; and how is the operation then to be performed? What is to be noted with respect to placing the decimal point in the sum, and in the sum total? 5. Add 56.12, .7, 1.314, 5837.01, and .15 together. Ans. 5895.294, 6. Add 361.04, .120, 78.0006, 101. 54, 8.943, and .3 Ans. 549.9436. together. MULTIPLICATION OF DECIMALS. Rule. Set down the multiplier under the multiplicand, as in simple multiplication; and multiply without any regard to the decimal points. When the operation of multiplying is completed, commence at the right hand figure of the product, and count off as many figures towards the left as there are decimal figures in the multiplier and multiplicand, and there place the decimal point. Note.-If the number of figures in the product is not so great as the number of decimal figures in both the multiplier and multiplicand, a sufficient number of ciphers must be placed to the left of the product, to make the figures in the product equal to the decimals in both factors, and the decimal part must then be placed to the left of the ciphers. Questions. How do you place the multiplier and multiplicand in multiplication of decimals? When the operation of multiplying is completed, how do you proceed to find where the decimal point is to be placed? What is to be noted when the number of figures in the product is not equal to the number of figures in both factors? Examples. 1. Multiply .322 by 6.12. 6.12 644 322 1932 1.97064 |