? 2. If 21 yards of cloth, 1yd. wide, cost 3 L. what is the value of 384 yds. 2 yds. wide ? Ans. 76L. 10$. 3. If 3 men receive 37% L. for 19į days labour, how much must 20 men have for 100 days Ans. 305 L. Os. 8 d. 83.d. 4. If so, in 5 months şain 2 IIL. interest , in what time will 13 L. gain 11 L.? Ans. in 9 months. 5. If the carriage of 60cwt. 20 miles, cost 14 dollars, what weight can I have carried 30 miles for 516 dollars ? Ans. 15 cwt. 37 144 DECIMAL FRACTIONS. a 75 6 2 5 1000) 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 to 10 are decimal fractions, and are expressed'by .5.75 .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. Thousand. Hundredth, 111111111 1 1 1 1 1 1 1 1 Decimals. Note.-Cyphers annexed to decimals, neither increase nor decrease their value; thus .5, 50, 500, being to oo 50 0 Tvo). are of the same value: but ciphers prefixed to decimals, decrease them in a tenfold proportion; thus, .5; .05,005, being to 1601067, are of different values. a 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; obserying to set the point in the sum exactly under those of the given numbers. EXAMPLES. .12 134 .21 .743 .345 .002 2.16 3.45 40,02 35.4 36.1 125.32 .14 2.1 4.12 15.4 76.36 120.16 425.04 .15 .75 : .92 63.25 25. 4. 1.554 242.45 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. EXAMPLES. .4562 56.12 .4314 5672.1 32.456 .316 1.242 .312 321.12 1.33 .1402 54.878 6. From 100.17 take 1.146 n. From 146.265 take 45.3278 8. From 4560. take .720 MULTIPLICATION OF DECIMALS. RULE. Multiply as in whole numbers, and point of in the product as many decimal places as there are in both factors. If there are not as many places in the product as there are decimal places in the factors, prefix ciphers to supply the deficiency EXAMPLES. 1. Multiply .612 by 4.12 2. Multiply 1.007 by .041 .612 1.007 4.12 .041 1224 612 2448 1007 4028 041287 2.52144 3. Multiply 37.9 by 46.5 Product '1762.35 4. Multiply 36.5 by 7.27 265.355 5. Multiply 29.831 by .952 28.399112 6. Multiply 3.92 by 196. 768.32 7. Multiply .285 by .003 .000855 8. Multiply 4.001 by .004 .016004 9. Multiply .00071 by 12} 200008591 Note.--Multiplication of decimals may be contracted 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 digits and set down the products, so that their right hand figures may call 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. Common way. 27.14986 27.14986 53014.29 92.41035 74434874 542997 2715 14 13574930 8144958 2714986 10859944 5429972 24.-34874 2508.9280 2508.9280650510 2.- Multiply 245.578263 by 72.4385, reserving 5 decimal places in the product. Prod. 17774.83330 3. Multiply 2.48264 by 725234, reserving 6 decimal places in the product. , Prod. .180049 DIVISION OF DECIMALS. RULE. Divide as in whole numbers, and from the right hand: of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor If the places of the quotient are not so many as the rule requires, supply the defect by prefixing ciphers. If at any time there be a remainder, or the decimal places in the divisor be more than those in the dividend, ciphers may be affixed to the dividend, and the quotient carried on to any degree of exactness, EXAMPLES 1. Divide .863972 by 92. 2. Divide. 4.13 by 572.4 92).863972.009391 572.4)4.1300000.00721+ 828 40068 3. Divide 19.25 by 3815 Quotient 15 4. Divide ,1606 by .44 3.65 5. Divide .1606 by 4.4 .0365 6. Divide .1606 by 44. ..00365 7. Divide 9. by ,9 10. 8. Divide .9 by 9. :.1 9. Divide 186.9 by 7.476 25. 10. Divide 234.70525 by 64.25 3.653 11. Divide 1.0012 by .075 13.34+ Division of decimals may be contracted thus: Take as many of the left hand figures of the divisor as will be equal to the number of integers and decimals in the quotient, and find how many times they may be had in the first figures of the dividend as usual. Let each remainder be a new dividend; and for every such dividend, leave out one figure to the right hand of the divisor, remembering to carry for the increase of the figures cut off, as in contracted multiplication. Note. When there are not so many figures in the divi: sor as are required to be in the quotient, begin the operation with all the figures, as usual, and continue it till the number of figures in the divisor, and those remaining to • be found in the quotient be equal, after which use the contraction. EXAMPLES. 1. Divide 2508.928065051 by 92.41035, so as to have 4 decimal places in the quotient. |