7. Two hundred and seventy-one billions, three hundred and twenty-one thousand five hundred and six millions, nine hundred and seven thousand, and twenty-five. 8. Twenty-five trillions, seventy-four billions, three hundred and fifty-one thousand two hundred and sixty-four millions, four thousand and twenty-one, Write in words the following numbers : The Romans and other ancient nations expressed their notation or numbers, by the seven following capital letters of the alphabet :-I. V. X. L. C. D. and M. It is still much used in the Scriptures, the Book of Common Prayer, Acts of Parliament, &c. ADDITION is the art of collecting two or more numbers or quantities into one sum. RULE. Place the numbers to be added under each other; observing that the units must be placed under the units, tens under the tens, hundreds under the hundreds, and so on. Add the figures in the column of units into one sum, and place the unit's figure of this sum under the column of units; carry the remaining figure or figures, if any, to the next column. Add the figures in this second column, together with the number carried, into one sum as before; place the unit's figure of this sum under the second column, and carry the tens or remaining figures to the next column, and so on, as in the following example : Add 94567, 896, 42784, 698, 27, and 1842 into one sum. 94567 896 42784 698 27 1842 140814 Here, the units 2, 7, 8, 4, 6, and 7 are placed under each other, and their sum is 34. Now the unit's figure of this sum is 4, which must be placed under the first column, and the 3 carried or added to the next column. Find the sum of the next column, together with the 3 which was carried; this sum is 41. Place down the 1 under the second column, and carry the 4 to the sum of the next or third column, and so on. The sum of the fifth or last column, together with the 1 carried to it, is 14; and as this finishes the addition, the 14 must be placed down. The above sum or example may be decomposed as follows: In the 1st row, the 9 stands for 90000 NOTE. The teacher can add as many examples as may be required to make his pupils perfect in this rule. 4. What is the sum of the following numbers:-13456, 78234, 56782, 43211, 23456, and 76544? 5. A person bought 4 bales of cotton goods; the 1st contained 325 yards, the 2nd 1200 yards, the 3rd 365 yards, and the 4th 326 yards: how many yards had he in the whole ? Ans. 2216 yards. NOTE.-The following method of proof, though not infallible, may be given: Add the figures in each row together, beginning with the top row, rejecting the nines contained in the sum, and set all the excesses at the end under each other; find the excess of nines in this line, and also the excess of nines in the sum total; then if these excesses be the same, the work is said to be right. 43464 34848 12345 146983 3 excess of nines. 4 Proof. The excess of nines in the sum total would be the same if the figures were reversed, as 389641, or if two or more figures were transposed, or if the value of one figure be too great, and that of another as much too little, or if a 9 be set down instead of a 0, or the contrary; the excess of nines in these cases will evidently be the same as the work was right; consequently it cannot be called a proof. SIMPLE SUBTRACTION. SUBTRACTION is finding the difference between any two given numbers. RULE.-1. Place the less number under the greater, so that the units may stand under the units, tens under the tens, and so on. 2. Begin at the right or unit's number, and take each figure in the lower line, when it can be done, from that above it, and set down the remainder. 3. But if any of the figures to be subtracted be greater than the corresponding figure in the top line, add ten to the upper figure, and then take the lower figure from the sum; observing to carry one to the next figure in the lower line, for the ten you borrowed or added, and proceed as before, till the whole be finished. Proof---Add the remainder to the less number, and if the sum be equal to the greater number, the work is right, EXAMPLE UNDER THE 1ST AND 2ND PARTS. From 873462 Take 712341 Remainder or Difference 161121 Proof 873462 EXAMPLE UNDER THE 3RD PART OF THE RULE. Take 281342 Rem. or Dif. 142074 Proof. 423416 Here, 2 from 6 and 4 remains; 4 from 1 we cannot, add 10 to 1, and the sum will be 11, from which take the 4, and 7 will remain; carry or add 1 to the 3, which will make 4, then 4 from 4 and 0 remains; 1 from 3 and 2 remains; 8 from 2 we cannot, add 10 to the 2, and the sum will be 12, from which subtract 8 and 4 will remain; carry or add one to the 2, which will make 3, then 3 from 4 and 1 remains. NOTE. Any number of questions of this kind may be added by the teacher. 5. What is the difference between 7854 and 9876? 6. What is the sum and difference of 45678 and 79628 ? Ans. :{ 125306 sum. 33950 dif. 7. A was born in the year 1794 and B in 1817 : how many years does A's age exceed that of B ? Ans. 23 years, 8. A was born in 1792 and died in 1841: what was his age when he died? Ans. 49 years. 9. Sir Isaac Newton was born in the year 1642 and died in 1727 how old was he at the time of his decease? : Ans. 85 years. 10. Homer was born 2749 years before the present year of our Lord 1842 how many years was that before the birth of Christ? Ans. 907 years. 11. Gunpowder was invented in 1344, and the Reformation commenced in 1517: how many years were there between, and how long is it since each event, this being 1842 ? Ans. 173 years between, and 498 and 325 since. 12. Printing* was introduced into England by Wm. Caxton in the year of our Lord 1474; Charles I., King of England, was beheaded January 30th, 1649; and Sunday schools first established in 1784: how long is it since each event to 1842 ? Ans. 368 years since printing was introduced. 193 since Charles was martyred. since Sunday schools begun. *The art of printing was invented by Laurentius of Haerlem, in the year 1430. |