Let the pupil be required to answer the following questions : 4+3=how many ? 2+5+1=how many ? 5+6+7+2=how many ? 8+9+2+1+7=how many ? 6+7+5+4+3+2=how many ? 1+2+4+3+5+7+6=how many ? EXAMPLES. 1. Where the sums of the several columns are less than ten ; OPERATION, Add together 2432, 3343 and 4122. Set the numbers under each other: units under units; tens under tens ; hundreds under hundreds; thousands under thousands. . Draw a line below the whole. Add first, the column of units. Set the sum 7 under the column of units; next add the tens; set the sum 9 under the column of tens-next add 3 3 4. 3 the hundreds; set the sum 8 under 4 1 2 2 the column of hundreds. Lastly, add 98 97 the thousands, and set the sum 9 under the column of thousands. The whole amount is, then, nine thousand eight hundred and ninety-seven. Add 6264, 2532 and 1203. Ans. 9999. Add 4132, 1001 and 1423. Ans. 6556. 2. Where the sums of the several columns equal or A co o Thousands. wo Hundreds. A co Tens. vw Units. exceed ten; OPERATION, Ten Thousands. Ooer Tens. What is the sum total of the following numbers : 3758, 4903, 7006, 3713, 3721. Place the numbers as directed in the preceding example. The sum of the numbers in the units' column is 21—that is, 2 tens and 1 unit. Set the 1 under the units' column, and carry the 2 to the next or tens' column. The sum of the tens' column thus increased is 10 4 9 0 3 tens; that is, 1 hundred and no 7 0 0 6 tens. Place a zero under the tens' 3 7 1 3 column, and carry the 1 to the hun 3 7 2 1 dreds' column. The sum of the 2 3 1 0 1 hundreds column, so increased, is 31 hundreds; that is, 3 thousands and 1 hundred. Set the 1 under the hundreds' column, and carry the 3 to the thousands' column. The sum of this column, so increased, is 23 thousands, or 2 tens of thousands and 3 thousands. Set the 3 under the thousands' column, and carry the 2 to the tens of thousands' place; or, what is the same thing, set down the whole of the sum of the last column. 10. From what has now been explained, we know that ten units are equal to one ten, ten tens are equal to one hundred, ten hundreds are equal to one thousand, and so on; ten of any order are equal to one of the next superior order. Hence, for adding numbers of the same denomination, we deduce this RULE. I. Place the numbers to be added under each other, so that units may stand under units, tens under tens, hundreds under hundreds, and so on for the higher orders. II. Commencing at the right, find the sum of the numbers in the column of units; if this sum is less than ten, place it immediately under the unit column; but if it equals or exceeds ten, see how many tens it contains, and how many units over ; write down the units under the units' column, and carry the tens to the next, or tens' column. In this way proceed with each column, observing to carry for every ten contained in such column, one to the column of the next higher denomination. When we reach the last column, its whole amount must be set down. How do wřite the numbers for addition? Where do you commence to add ? If the sum is expressed by a single digit, how do you dispose of it? When it equals or exceeds ten, how do you proceed? What is the rule with regard to carrying? How do you proceed when you come to the last column ? you EXAMPLES. (1.) 56430 12798 34457 21325 (2.) 7921341 82345768 79013265 7890275 177170649 amount. 125010 amount. PROOF OF ADDITION. 11. The method of proving, or testing the work of addition, is generally to commence at the top of the respective columns and add downwards, carrying one for every ten as before ; if the sum is the same as when the columns were added upwards, the work is then supposed to be correct. This proof is not infallible, since mistakes of figures. When there are more than nine places of figures, it will be convenient to divide them into periods of three figures each, as in the following By this table we discover that each period, or group of three figures, takes a new name, by which means the numeration of all numbers is made to depend upon that of three figures. 6. The above method of numerating, by giving to each period of three figures an independent name, is due to the French. There is another method, sometimes used, called the English method. It consists in giving a new name to each period of six figures. The French way is the sim 467743486921785412123456489 45654213400100205437 1347835674116 periods of three figures, the following numbers : 7. After the pupil has carefully examined this table, How many do the English connect in a period ? Which method is to be preferred ? By the French method of numerating, how many figures are connected in a period ? ENGLISH METHOD. FRENCH METHOD. Octillions. Tens of Septillions. Quintillions. Hundreds of Trillions. Trillions. Hundreds of Millions. Tens of Millions. Tens of Thousands. Hundreds. TABLE. methods at one view in the following |