lowing table in the first place; then to take the mental exercises that follow, and study them faithfully before commencing with a slate. Indeed, the author would advise, that the tables, together with the mental exercises, which stand at the beginning of each of the four simple rules, be first studied; and that the beginner then turn back and review the whole. ADDITION TABLE. The signs plus and minus, &c. are introduced into the following tables, that the scholar may early learn the use of them. He will therefore turn back to Notation, if he does not recollect their use. In reciting this and the following tables, the teacher should be careful that the scholar, as he repeats his answers, perform the necessary mental operation; he must teach his pupil to think. MENTAL EXERCISES IN ADDITION. If you borrow 6 dollars at one time and 3 at another, how many will you have? 6 and 3 are how many? A pays you 3 dollars, B 4, and C 5; how many do they all pay you? 3+4+5= how many? If you pay away 6 cents at one time, 4 at another, and 3 at another, how many do you pay away? 6+4+3= how many? If you buy twelve apples for 9 cents, and a pint of chesnuts for 4, how many cents do the apples and chesnuts cost? 9+4= how many? John gave Henry 8 apples at one time, 6 at another, and 4 at another; how many did he give him? 8+6+4= how many? Lent ; my brother 10 dollars at one time, 6 at another, and 4 at another how many dollars did I lend him? 10+6+4= how many? Alfred has four brothers; to one, he gave 11 pears, to another, 9, to another, 6, and to another, 3; how many pears did he give away? 11+9+6+3 = how many? He also gave his two sisters 5 each; how many did he give to both brothers and sisters? 11 + 9 + 6 +3 +5 +5 = how many? A man bought four bushels of corn for 3 dollars, six bushels of oats for 2 dollars, and 9 bushels of wheat for 12; how many bushels of grain did he buy, and how many dollars did the whole cost him? 4+69 how many? 3+2+12= how many? John has 9 dollars; James, 12; and Joseph, 7; how many have they all? 9+12+7= how many? Peter gave a poor man 11 cents; Charles gave him 12 cents; Henry, 10; and George, 8; how many did they all give him; 11+ 12+10 + 8 = how many? A man was three days performing a journey; the first day he traveled 13 miles; the second day, 14; and the third, 15; how far did he travel? 13 +14 + 15 = how many? How many sums will you have done, if you do 12 to-day, 15 to-morrow, and 18 the next day? 12+15+18=how many? How many are 3+4? 13+4? 23+4? 33+4? 43+4? 53+4? 63+4? 73+4? 83+4? 93+4? How many are 4+4? 14+4? 24+4? 34+4? &c. How many are 5+4? 15+4? 25+4? 35+4? &c. How many are 6+4 ? 16+4? 26+4? 36+4? &c. How many are 7+4? 17+4? 27+4? 37+4? &c. How many are 4+4? 4+14? 4+24? &c. 4+5? 4+15? 4+25 ? &c. 4+6? 4+16? 4+26? **&c. 4+7? 4+17? 4+27? &c. How many are 5+5? 5+15? 5+25? &c. 5+6? 5+16? 5+26? &c. 6+6? 6+16? 6+26? &c. How many are 7+7? 7+17? 7+27? &c. 8+8? 8+18? 8+28? &c. 9+9? 9+19? 9+29? &c. How many are 10+10? 10+20? &c. 11+5? 11+15? 12+4? 12+14? &c. Questions of this character may be proposed to any extent, and should in no instance be omitted until the scholar can add without hesitation. Others of a more promiscuous character should likewise be proposed, such as the following: 7+4+6=how many? 2+1+9+6+7+6=how many? 5+6+9+3=how many? 6+4+2+8+1+3+5+7+9= how many? 11+9+6+12= how many? 7+6+9+8= how many? 8+8+6+6+4+4=how many? 7+7+9+9= how many? 2+4+6+8+10+12=how many? The scholar may now commence the use of the slate and pencil, or the practice of written arithmetic. The first consideration to which his attention should here be directed, is, that like things only can be added to or subtracted from each other. It would be absurd to attempt to add together books and chairs, to see how many books, or how many chairs the whole would make; the number of each would evidently remain unaffected. If, however, we add books to books, we obtain a number greater than either of the original numbers; that is, just equal to them both. Neither can we add units to tens; for the amount would be neither units nor tens; but units must be added to units, tens to tens, and hundreds to hundreds, and so on. But ten units make one ten, ten tens make one hundred, and ten hundreds make one thousand, &c.; that is, simple numbers increase and decrease in a ten-fold ratio. Hence 10 in the column of units is equal to 1 in the column of tens; and 10 in the column of tens, is equal to 1 in the column of hundreds. If, then, in adding up the column of units the whole should amount to just 10, it is obvious that nothing is lost, if these 10 units are converted into 1 ten, and the 1 ten added to the column of tens; for 10 units = 1 ten. The same is true of other denominations. Therefore the following General Rule will be found applicable to Simple Addition: 1st. Write down the numbers, placing units under units, tens under tens, &c. 2d. Draw a line underneath, and commence at the right hand and add together all the figures in the first column. 3d. If the sum be less than 10, set it down at the foot of that column; if it be 10, or more than 10, it will consist of two figures at least; set down the right hand one as before, and add the left hand one to the next column, it being in all cases so many tens, when compared with the figures added. 4th. Continue to perform the same operation with the remaining columns, observing only to write down the whole amount of the left hand column. 5th. To detect any error that may have been committed, commence again and add each column downwards; if the same numbers are obtained by each operation, the work is probably right. Now to apply this rule, let us add together the four following numbers, viz. 1234; 2345; 6420; and 5796. The rule says, write these numbers with units under units, tens under tens, &c. thus: 1 2 3 4 2 3 4 5 6420 5796 15795 Now to add these numbers, I commence at the right hand, and first add together the unit figures; viz. 6, 0, 5, 4; the sum I find to be 15 units, equal to 1 ten and 5 units; I write down the 5 units, but add the 1 ten to the next column; thus, 1 added to 9 is 10, and 2 are 12 and 4 are 16 and 3 are 19; as before, I write down the 9, and add the 1 to the next column; this being added gives the amount 17; the 7 is written down and the 1 again carried to the next and last column; and here the amount is 15, which being the last column, the whole number is written down. This operation gives the amount of the four numbers, 15795. The scholar will readily comprehend the nature of Simple Addition; viz. that it consists in uniting two or more numbers of the same denomination, so as to find their amount. The scholar will carefully examine the following sums, which are added, to see if he obtains the same result. 2. 8 47 39 6 3 6 4 8 69 4 8 2 4 3 6 6 2 2 4 3 9 2 3 1 7 1 4 0 3. In this second example, in the unit column, there are 3 to carry, because there are 3 tens or 30. For the same reason there are 2 to carry in all the remaining columns but one. 4. 1 2 3 4 5 6 7 8 9 3 3 3 3 3 3 3 3 3 0 97963 65 5 6 3 6 9 79 1 3 5 7 9 1 2 4208-642 2 1 3 5 7 9 1 3 3 5 5 7 7 9 8 8 6 6 4 4 8 5 9 6 3 8 1 6 4 6 7 4 3 6 4 5 7 9 6 3 78 2 2 3 9 2596 7. 1798 6 7 0 6 1 2 4 3 5 6 7 2 1 2 3 4 5 8 4 6 37 38 5 7 3 9168 9 1 5 6 4 2 3 8. 9 1 7 6 4 3 5 5 6 8 3 2 1 4 2 3 4 5 6 7 8 0 1 2 3 4 5 6 4 0 1 1 3 926 9. 3 4 5 7 096 6 17 2 8 349 28 394 5 6 3 5 6 8 3 1 2 3 4 10. 70 8 1963 4 6 4 7 5 3 278 8 6 5 4 2 3 6 5 2 3 4 5 6 7 8 9 |