Write the following Sums in Figures. 1. Seventeen, and four tenths. 2. Twenty-five, and twenty-five hundredths. 3. Six, and five thousandths. 4. Four, and one millionth. 5. Seventy-five, and twenty-three hundredths. 6. Forty, and eight thousandths. 7. Sixty-nine, and five tenths. 8. Nine millionths. 9. Twelve, and six hundredths. ADDITION OF DECIMALS. RULE. Q. How do you add decimals? A. The given numbers must be placed according to their local value, or the value of their places, whether mixed, or pure decimals, so that tenths will stand directly under tenths, hundredths under hundredths, thousandths under thousandths, &c. The numbers must then be added the same as whole numbers, and as many places must be pointed off for decimals, at the right hand, as shall equal the greatest number of decimal places in any of the given numbers. EXAMPLES For Theoretical Exercise on a Slate. 1. Add 4 tenths 6 tenths. and 8 tenths together. Ans. 1,8 EXPLANATIONS. 1,8 Ans. In this example, you add the 8, 6, and 4 tenths together, which make 18 tenths, or 1 unit and 8 tenths, because ten tenths are equal to one unit, or one; and, therefore, you point off below the given points, for when the tenths exceed nine tenths they equal a unit; and the number of figures must increase, and this increase must be units. The reason why you add the same as in whole numbers is very evident, because as the parts diminish in a tenfold proportion from the left hand to the right, so they must increase in a tenfold proportion from the right hand to the left. 2. Add 1,4, 4,25, 7,45, 2,605,,50,05. Ans. 16,255. EXPLANATIONS. 1,4 4,25 7,45 2,605 ,50 You will remember, that the first thing to be done is to place the whole numbers under each other, as in Addition of whole numbers, and the tenths under tenths, hundredths under hundredths, &c. You must begin with the decimal at the right hand to add; carry one for every ten as in whole numbers, and in the final product you must point off as many figures at the right hand for decimals as shall equal the 16,255 highest number in any of the given numbers to be added. ,05 3. Add six tenths, ninety-nine thousandths, thirty-seven hundredths, nine hundred and five thousandths, and twentysix thousandths. Ans. 2. 4. Add five thousandths, four hundredths, forty-five thousanaths, and four tenths. Ans. ,49. 5. Add four tenths, seven hundred and forty-five thousandths, thirty-four ten thousandths, and fifty-six hundredths. Ans. 1,7084. 6. Add 71,467, 27,94, 16,084, 98,009, 86,5. Ans. 300. 7. Add 19,041, 105,7, 648,006, 19,4, 1119,05. Ans. 1911,197. 8. Add $10,09, $96,75, $144,17, $695.832, $650,253, ARS. $1597,095. 1 Q. How do you substract decimals? A. The given numbers must be placed the same as in Addition of decimals, with the less number under the greater, and substracted as whole numbers. Point off the decimals in the difference, or answer, as directed in Addition. EXAMPLES For Theoretical Exercise on a Slate. 1. From 75 hundredths take 25 hundredths. Ans. ,50. EXPLANATIONS. You must first place the less number under the ,75 greater, with tenths under tenths, hundredths under 25 hundredths, &c. Begin at the right hand figure, and substract as in whole numbers. As decimals de-,50 Ans. crease in a tenfold proportion, you will at once see the propriety of borrowing ten and adding it to the upper figure, and of carrying one to the next figure, as in whole numbers, when the figure in the lower line is larger than the apper. After you have substracted the lower line from the upper, as in whole numbers, you must, if there be units, or whole numbers, in the given sum, point off as many decimals in the difference, or answer, as the highest number of decimals in either the minuend, or subtrahend, of the given sum. 2. From one and six tenths take four tenths. 2 tenths. Ans. 1 and 3. From nine tenths take twenty-five hundredths. Ans.,65. 4. From one take one millionth. Ans. ,999999. 5. From forty-five and six tenths take thirty-six and twentyfive hundredths. Ans. 9,35. 6. From 5 dollars take 6 mills. Ans. $4,99,4. 7. From 6 tenths of a gallon take 35 hundredths of a gallon. Ans. ,25 of a gallon. 8. From 5 yards take 25 hundredths of a yard. Ans. 4,75 Q. How do you multiply decimals? A. They must be multiplied the same as whole numbers, and as many figures must be pointed off. from the right hand of the product, as there are decimal places in the multiplicand and multiplier. When there are not figures enough in the product, ciphers must be prefixed to the left hand of the product to supply the deficiency. EXAMPLES For Theoretical Exercise on a Slate. 1. Multiply 20,4 by,4. Ans. 8,16. EXPLANATIONS. 20,4 ,4 In this example, you multiply by 4, and the product is 816, and you must point off two figures at the right hand, the 16, for decimals, because there are two decimal figures in the multiplicand and multiplier; and the 8,16 product will be 8 units, or whole numbers, and,16 hundredths. The reason of your pointing off is very obvious, for the multiplier, 4 tenths, is only one tenth part the value it would be if it stood in the place of units; and, therefore, the product can have only one tenth part the value it would have if it were multiplied by four units; and by pointing off two figures from the right of the product, you give it one tenth the value. Thus, if it were not pointed, the product would be 816; but when pointed, it is only 8 units, and 16 hun., which 8 is, as you will readily perceive, one tenth part of 80. 2. Multiply 55 by,5. Ans. 27,5. 3. Multiply,004 by ,003. Ans.,000012. 4. Multiply 7,063 by 4,35. Ans. 30,72405. 5. Multiply 25,238 by 12,17. Ans. 307,11646. 6. What will 10,5 pounds of butter cost at 25 cents a pound? Ans. $2,625, or $2,62 cents, 5 mills. 7. Multiply 18,6 by one thousandth. Ans.,0186. 8. Multiply 2461 by,0529. Ans. 130,1869. RULE. To multiply by 10, 100, 1000, &c., remove the separatrix as many places to the right hand as the multiplier has ciphers. Thus,,125 multiplied by 10, it would be 1,25; multiplied by 100 it would be 12,5, and so on.. |