RULE.-State the question as in whole numbers, then invert the divisor, and multiply it by the product of the other two. EXAMPLE. 1. If 14 yards of kerseymere cost 13s. 6d., what will 4 yards cost? 71 42 = 4026 = 1 £2. 2s. 9d. Ans. = 2. If of a yard cost £3., what will a yard cost at that rate? 3. If 5 4. If value of ? Ans. 4s. 5 d. yards cost £., what will 24 yards cost? Ans. 6s. 64d... 23. of a ship be worth £20. 5s. Od., what is the 5. If of a ship be worth the value of of her? Ans. £202. 10s. Od. £252. 12s. 6d., what is Ans. £294. 14s. 7d. 6. If three yards cost £24., what will 10 yards cost at the same rate? Ans. £9. 12s. Od. • To divide a fraction by an integer-divide the numerator, if it be divisible; if not, multiply the denominator. 7. If of a steam boat be worth £73. 1s. 3d., what part of her is worth £250. 10s. Od. ? Ans.. 8. By working 12 hours in the day, A can do a piece of work in 7 days, and B can perform the same in 5 days, how long will it serve them when they work together? Ans. 2 days 11 hours. 9. Divide a guinea among A, B, and C, so that their shares may be in proportion of,, and respectively. Ans. A 9s. 8d.... B=6s. 54d.. C4s. 10d...7. •13. 10. Supposing a brewer to have 4 syphons, one of which will empty his cooler in a quarter of an hour, another in half an hour, one in three quarters, and the other in an hour, in what time would they empty it, all running together? Ans. 7 minutes. 11. How many yards, at 3s. 3d. a yard, are equivalent to 60 yards, at 4s. 4d. a yard? Ans. 80 yards. of a yard wide, will Ans. 23 yards. 13s. 4d., what 12. What quantity of shalloon line 11 yards of cloth, 14 yard wide? 13. If 174 yards of cloth cost £43. should be charged an ell English to gain £4. 7s. 4d. by the whole ? 14. If 6 yards of cloth much at wide will line it? 15. If of a crown buy yards will 7 guineas buy? Ans. 6s. 10 d. wide will make a cloak, how Aus. 915 yards. of an ell English, how many Ans. 27. DECIMAL FRACTIONS. A decimal fraction is a fraction whose denominator is 10, 100, 1000, &c., or an unit with as many cyphers after it as there are figures in the numerator, which numerator only is put down with a point before it. Thus: .5 five tenths. 5.25 twenty-five hundredths, &c. Decimals express the parts of an unit in the same manner as whole numbers express the number of units, as may be seen by the following table: Whole numbers. Decimal parts. 7 6 5 4 3 2 1 2 3 4 5 6 7 Parts of Tens. Parts of Hundreds. Parts of Thousands. Parts of X Thousands. Parts of C Thousands. Parts of Millions. Millions. Tens. C of Thousands. Thousands. Hundreds. Units. X of Thousands. 1. From the above table it appears that as whole numbers increase in a ten-fold proportion to the left hand, decimal parts decrease in a ten-fold proportion to the right hand. 2. Cyphers placed before decimal parts, decrease their value, by removing them farther from the decimal point, or unit's place; thus, .5 is 5 parts of 10, or; but .05 is 5 parts of 100, or ; .005 is 5 parts of 1000, or 5, &c. 10009 5 3. Cyphers after decimal parts do not alter their value, for .5 = .50 = .500 = 5 To transform a Vulgar Fraction to an equivalent Decimal Fraction. RULE.-Annex cyphers to the numerator, and divide by the denominator, the quotient will be the decimal fraction required. * A finite decimal is one that ends at a certain place. + An infinite decimal is one that does not terminate; and if the same figures are repeated from the decimal point, it is called a pure repeater, the last of which is marked with a dot. It is not necessary to take them farther than one figure, becanse 3 is equi, alent to .3333, &c. ADDITION IN DECIMALS. RULE.-Set down the numbers under each other according to the value of their places, and the decimal points will stand exactly under each other: then add them up as in whole numbers. EXAMPLE. 1. Add 7.53.527+25.036+1.1111+ 100 together. 7.53 25.036 1.1111 100. 134.2041 Ans. • When there are figures before the repeater, it is called a mixed repeater. † When two or more figures repeat, it is called a circulating decimal. If there is a figure or figures between the decimal point and the circulating figures, it is called a mixed circulate; every infinite decimal would circulate, were it carried out far enough, but when the circle does not readily appear, the 5th or 6th figure is usually marked with a 2. Add 1.64 + 32.543 + .023 +.2576 + 324 together. Ans. 358.4636. 3. Add 643.037 +543.4 +2.76543+.4 together. Ans. 1189.60243. 4. Add 75.0756+3254.072 +3.543.576+.004 together. Ans. 3333.2706. 5. Add 3.20076 +27 + .0058 + 7238.5 + 12.75 +.54344 together. Ans. 7282. RULE. Place the numbers as in addition, having the decimal points under each other, and subtract as in whole numbers. MULTIPLICATION OF DECIMALS. RULE. Place the factors and multiply them as in whole numbers, and from the product to the right hand, point off as many figures for decimals, as there are decimals in both factors; but should there not be as many figures in the product, prefix as many cyphers to the left hand as are wanted. Cyhers to the right of decimals are of no value. |