Practical Questions in Time. 1. Aman hired a servant for 6 years, 4 months, 3 weeks, 6 days; and he stayed 7 years, 6 months, 3 weeks; how much longer did he stay than he first agreed to? F Ans. 1 yr. 1 mo. 3w. ld. 2. What is the difference between 21 years, 6 months, 3 weeks, 4 days, 12 hours; and 19 years, 9 months, 2 weeks, 6 days, 21 hours? Ans. 1 yr. 10 mo. 0 w. 4d. 15 h. CASE II. When the time is expressed in years and callender months and days.* RULE. Write down the latest date first, (consider whether the month is the first, second, or third, &c. if it is January, write in the column of months; if it is February, write 2; if March 3, &c.; and after writing the months, write the day of the month) and then write down the other numbers under those of the same denomination; subtract, and the remainder is the difference be tween the two dates. Examples. 1. What is the difference of time between the 16th day of February 1800; and the 19th day of May 1806? Years mo. d. NOTE. In this example the latest year is written first, May being the fifth month, 5 is put in the column of months, and the day of the month, in the column for days: and then the other denominations are put under those of the same name. 2. How long between the 15th day of June 1729, and the 30th day of August 1806, inclusive? Ans. 77 years, 2 months, 15 days. * OBSERVE THE FOLLOWING TABLE. January is the first month. February May June July is the 7th month 2d 3d 4th October 5th November 6th December 8th 9th 10th - 11th 3. I was born the 7th day of May, 1777; what is my age, it being the 20th day of June 1810? Ans. 33 years, 1 month, 13 days. 4. A. gave B. his note on interest, dated the 21st of August 1804; on the 29th day of November 1809, the note was paid: I demand the time that the note was at interest. Ans. 5 years, 3 months, 8 days. DECIMAL FRACTIONS. DEFINITION. Decimal Fractions are parts of whole numbers, and are separated therefrom by a peint called the separatrix, thus, 12.5: which is 12 and 5 tenths, or 12; all the figures which stand at the left of the separatrix are whole numbers; those on the right, are frac tions. An unit is supposed to be divided into ten equal parts, and the figure next the separatrix on the right expresses the number of those parts; again, one of these parts is supposed to be divided into ten more equal parts; and the next figure in decimals expresses the number of those parts, &c. Thus decimals decrease in a tenfold proportion, as they depart from the separatrix; thus 5 is 5 tenths; 05 is 5 hundredths; and ·005 is 5 thousandths, &c. Cyphers placed at the right hand of deci mals do not alter their value ·5 50 and 500 are decimals of the same value and equal to 5. DECIMAL NUMERATION TABLE. NOTE By the table it is evident that the value of figures increase in whole numbers, as they depart from the separatrix; and in the fractions, the value of the figures decrease as they depart from the separatrix. ADDITION OF DECIMALS. RULE. Write down the several numbers to be added, so that units may stand under units; tens under tens; hundreds under hundreds; and the fractions must stand tenths under tenths; hundredths under hundredths, &c. The several decimal points must stand directly under one another, then add the several sums together in the same manner as in Simple Addition. Separate the sum total by placing the separatrix under those directly above. 1. Add 504-29, 64-1, 23-09 and 55.6 together. Ans. 647-08 NOTE.-Dimes, cents and mills are decimals of a dollar; one dime is one tenth; one cent is one hundredth, one mill is one thousandth: therefore the addition of American money, is the addition of decimals. 2. Add $1327-64 cents; $2341 96 cents 9 mills: and $1572 21 cents together. Ans. $5241.819. 3. Add 46-969, 6.01 and 946 together. D Ans. 53.925. SUBTRACTION OF DECIMALS. RULE. Write down the largest of the two numbers first, then write down the smallest under it, observing to place the separatrix under each other; then subtract exactly as in Simple Subtraction. MULTIPLICATION OF DECIMALS. RULE. Multiply exactly as in whole numbers, and from the right of the product point off as many figures for decimals as are equal to the decimal figures in the multiplicand and multiplier, counted together; If at any time there are not so many figures in the product, as this rule requires, supply the defect by prefixing cyphers, to the left of the products. NOTE. In the first example there being three decimal figures in the two factors, three figures are pointed off for decimals in the product; in the second example there are eight decimal figures in both factors, and the product consists only of seven figures, therefore I prefixed one cypher and pointed all off for decimals. 1. How much is the product of 29.5 multiplied by 96? Ans. 28.32. 2. How much will 1000 pounds of butter come to, at 114 cents per pound? Ans. $115. 3. How much will 64.5 bushels of corn come to at $1.12 cts. per bushel? Ans. $72.24 cts. DIVISION OF DECIMALS. RULE. Divide exactly as in whole numbers, and from the right hand of the quotient point off as many figures for decimals, as the decimal figures in the dividend exceed the decimal figures in the divisor; if there are not so many figures in the quotient as this rule requires, the defect must be supplied by prefixing cyphers to the left of the quotient; if there are more decimal figures in the divisor than in the dividend, place as many cyphers to the right of the dividend, as will make them equal, and the quotient is whole numbers till the dividend is all brought down; if a remainder still remains annex cyphers and continue the division and the quotient thence arising will be decimals. Examples. 1. It is required to divide 34-21 by 12.1. 12.1)34-21(2·8 Ans. 242 1001 968 33 rem. NOTE. There being one more decimal figure in the dividend, than in the divisor, one figure is pointed off from the right of the quotient for deci |