EXAMPLES. 1. If a yard of cloth, a yard wide, cost L. what is the value of yard, 14 yards wide, of the same quali ty? yd. yd. :: L. : lyd. Zyd. 70 2x1x=76% 7. 76÷31-33=3L.=13s. 4d. Answer. 2. If 24 yards of cloth, 13yd. wide, cost 33L. what is the value of 384yds. 2yds. wide? Ans. 76L. 103. 3. If 3 men receive 8 L. for 19 days labour, how much must 20 men have for 100 days? Ans. 305L. Os. 8d. 4. If 50L. in 5 months gain 2L. interest, in what time will 13 L. gain 1L.? Ans in 9 months. 5. If the carriage of 60cwt. 20 miles cost 14 dollars, what weight can I have carried 30 miles for 57% dollars? Ans. 15cwt. DECIMAL FRACTIONS. A decimal fraction is a fraction whose denominator is 1, with as many ciphers annexed as there are places in the numerator, and is usually expressed by writing the numerator only with a point prefixed to it: thus fo, too, too, are decimal fractions, and are expressed by .5, .75, .625. 625 A mixed number, consisting of a whole number and a decimal, as 25%, is written thus, 25.5. As in numeration of whole numbers the values of the figures increase in a tenfold proportion, from the right hand to the left; so in decimals, their values decrease in the same proportion, from the left hand to the right. which is exemplified in the following TABLE. -Hundred million. Hundred thousand. -Unit. Hundredth. -Hundred thousandth. -Thousandth. -Ten thousandth. -Thousand Millionth. -Tenth. -Ten Millionth. 1 1 Whole numbers. 50 Decimals. Note.-Ciphers annexed to Decimals, neither increase nor decrease their value; thus, .5, .50, .500, being, 100, 100, are of the same value: but ciphers prefixed to decimals, decrease them in a tenfold proportion; thus .5, .05, .005; being fo, 180, 1800, are of different values. ADDITION OF DECIMALS. RULE. Place the given numbers according to their values, viz. units under units, tenths under tenths, &c. and add as in addition of whole numbers; observing to set the point in the sum exactly under those of the given numbers. 6. Add .5, .75, .125, .496, and .750 together. 7. Add .15, 126.5, 650.17, 940. 113, and 722.2560 together. 8. Add 420., 372.45, .270, 965.02, and 1.1756 together. SUBTRACTION OF DECIMALS. RULE. Place the numbers as in addition, with the less under the greater, and subtract as in whole numbers; setting the point in the remainder under those in the given numbers. Multiply as in whole numbers: then observe how many decimal figures there are in both factors, and point off that many figures, for decimals, in the product. If there are not so many figures in the product as there are decimal figures in both factors, préfix ciphers to supply the deficiency. Note.-Multiplication of decimals may be contract ed thus: Write the units place of the multiplier under that figure of the multiplicand whose place you would reserve in the product; and dispose of the rest of the figures in a contrary order to what they are usually placed in. In multiplying, reject all the figures that are to the right hand of the multiplying digit, and set down the products, so that their right hand figures may fall in a straight line below each other; observing to increase the first figure of every line with what would arise by carrying 1 from 5 to 15, 2 from 15 to 25, &c. from the preceding figures when you begin to multiply, and the sum is the product required. EXAMPLES. 1. Multiply 27.14986 by 92.41035, so as to retain only four decimal places in the product. Contracted. 27.14986 53014.29 24434874 542997 108599 2715 81 14 Common way. 27.14986 92.41035 13574930 8144958 2714986 10859944 5429972 24434874 2508.9280650510 2508.9280 2. Multiply 245.378263 by 72.4385, reserving 5 decimal places in the product. Prod. 17774.83330. 3. Multiply .243264 by .725234, reserving 6 decimal places in the product. Prod.180049. DIVISION OF DECIMALS. RULE. Divide as in whole numbers; then observe how many more decimal figures there are in the dividend than in the divisor, and point off that many figures, for decimals, in the quotient. If there are not so many figures in the quotient as the rule directs to be pointed off, prefix ciphers to supply the defect. If, after dividing, there be a remainder, ciphers may be affixed to the dividend, as decimal figures, and the quotient carried on to greater exactness. If there are more decimal figures in the divisor than there are in the dividend, the number of decimal figures in the dividend must be increased by affixing ciphers. Note 1.When a whole number is to be divided by a greater whole number, ciphers must be affixed to the dividend, as decimal figures. Note 2.-When any whole number is divided by another, if there be a remainder, ciphers may be affixed to the dividend, and the quotient continued. |