(6.) Seven tenths; fourteen hundredths; sixty-seven hundredths. (7.) Nine hundredths; nine thousandths; three hundred and five thousandths. (8.) Five hundred and fifty-six thousandths; seven hundred and eighty-three thousandths. (9.) Five thousand and seven millionths; sixty-four millionths. (10.). Twenty-three and twenty-three hundredths; twelve and ninety four hundredths. (11.) One thousand and five, and one thousand and five tenths of thousandths.. (12.) Seven millions and seventeen millionths; nine millions and nine, and nine millionths. (13.) Two hundred and ten millions, seven thousand and four, and eight hundred and three millionths. (14.) Nine hundred millions, and five hundred and fifty-one thousandths of millionths. (15.) Three tenths, three hundredths, three thousandths, and three tenths of thousandths. ADDITION. 13. To add, is to collect several numbers into one sum. RULE. Place the numbers under each other, so that units may be under units, tens under tens, &c. Then begin on the right, and add up each column separately, putting down the amount, if not more than 9; but if more, see how many tens are contained in it, and put down only the remainder, carrying one for each. ten to the next column. Place the decimal point in the sum or answer under the decimal point in the several numbers that have been added up. Thus, This is worked out simply according to the rule above, but the reason is obvious. Eight hundredths and four hundredths are twelve hundredths, or two hundredths and one tenth; put down the two hundredths under the hundredths, and carry one tenth to the tenths, then adding up again, one tenth, two tenths, and seven tenths, are ten tenths, or one unit; put down 0 tenths, and carry one unit; then again, one unit, and one unit, and five units, are seven units, and so on. (2.) Add 59413.042, 86.7, 431, and 7.83569. 59413.042 86.7 431 7.83569 59938.57769 ANSWER. (3.) Add 7651, 23790, 4453, and 769. 14. Proof of the work in whole numbers. Add together all the figures in the first row, reject all the nines contained in their sum, and put down the remainder in the same line. Do the same with all the other rows; then find the sum of all the remainders, and the excess of nines in this sum ought to equal the excess of nines in the tota 4 5 6 7 8 9 10 11 12 13 6 7 8 9 10 11 12 13 14 5 6 7 8 9 10 11 12 13 14 15 7 8 9 10 11 12 13 14 15 16 10 11 12 13 14 15 16 17 18 This Table is used thus: 1 and 1 are 2, 1 and 2 are 3, 1 and 3 are 4, &c. 2 and 1 are 3, 2 and 2 are 4, 2 and 3 are 5, &c. EXAMPLES. (1.) Add together 352, 451, 7639, 204. Answer, 8646. 71876, 2350, 1701, 9876. 25, 179, 8763, 54901, 6. 8825, 18934, 137984, 6521, 86. 31925, 80641, 59, 83954, 772. 421,99, 89765, 84, 900909,888888. 18.35, 29.764, 843.54, 81.1, 14.93. 8761.41, 8.7614, 87.614, 8761.4, 87614. 90.09, 883.021, 59.4976, .0008, 80809.2. (10.) Add together 88.47613, 5943.0219, 750.40059, 84.3, .76, 5093, 845.845. 5317.605, 1264.3921, 85648.909, 1.86009, 75.7575. (14.) Sir Isaac Newton was born in the year 1642, and lived to his eighty-fifth year. In what year did he die ? How (15.) In the House of Commons there are 471 English Members, 29 Welsh, 53 Scotch, and 105 Irish. many are there altogether? (16.) The distance from London to York is 196 miles, from York to Newcastle 82, and from Newcastle to Edinburgh 121. What is the whole distance from London to Edinburgh? (17.) In a game at cricket, the first player on one side made 27 runs, the next 45, the third 19, the fifth 63, the sixth 9, the eighth 17, the ninth 1, and the rest none. How many runs were made altogether? (18.) Add eight hundred and five to eighty-five thousand. (19.) Add nine hundred thousand and seventeen to eighty-five thousand and forty-one thousandths. (20.) Add together eighteen millions, four hundred and one, sixty-four thousand and sixty-four, fifty-seven and three hundred and two thousandths, and forty-one hun dredths of thousandths. (21.) Add together five hundred and eight millions, forty millions and forty, nineteen thousandths, and eighty-nine tenths of thousandths. SUBTRACTION. 16. To subtract one number from another is to find their difference, or to find a number which added to the first will produce the second. Such a number is called the remainder. The number to be subtracted is called the subtrahend, and the number from which it is to be subtracted the minuend. RULE. Place the number to be subtracted under the other, so that units may be under units, tens under tens, &c. Begin at the right hand, and take each figure in the lower line from that above it, and set down the remainder; but if any one of these figures be greater than that above it, add ten to the upper one, and then take the lower figure from it, observing in this case to carry one for the ten that was borrowed to the next lower figure. Place the decimal point in the answer under the decimal points in the given numbers, as in Addition. Thus, (1.) 85.49 32.57 52.92 Here seven hundredths taken from nine hundredths leave two hundredths, put down two; then, five tenths cannot be taken from four tenths, add ten tenths or one unit to the four tenths, which make fourteen tenths, then five tenths from fourteen tenths leave nine tenths. Now, as we added to the upper line one unit, or ten tenths, we must add to the lower line one unit, which makes the two units to become three units; then take three units from five units, and so on. Hence it appears that this borrowing ten and carrying one is really adding the same amount to each line, so that the relative value of each is not altered. |