CHAPTER II. ADDITION.- -SECTION I. THE object of addition is to unite two or more numbers into one. Thus, if John has 4 marbles and James 3, they will have 4 and 3, or seven marbles between them. The number 7 is called the sum of 4 and 3, and the operation by which it is found is called addition. We will begin with the most simple case, namely, the addition of two or more numbers of one figure. If we are required to add the numbers 5 and 3, we may hold up three fingers, and counting from 5, say six, seven, eight; the sum is 8. Again, if we wish to add the numbers 4, 2, and 3, first hold up two fingers, and counting from 4, say five, six; 6 is the sum of 4 and 2 ; now hold up three fingers, and counting from 6, say seven, eight, nine; 9 is the sum of 4, 2, and 3. Examples.-Apply this method to find the sum of the following numbers : and A. (1) 5 2. () 8 and 2. (17) 3, 4, and 5. (2) and 3 4. (10) 6 and 5. (18) (3) 6 and 3. (11) 8 and 6. 5, 2, and 6. (19) 6, 4, and 5. and 7. (20) 4, 8, and 6. (21) 9. (8) 5 and 4. (16) 4, 3, and 2. (24) 7, 9, and 3. 9, 8, and 5. 7, 9, and 8. The above process may be followed in finding the sum of any two or more numbers of one figure; but if the pupil will learn the addition table, which contains the sum of any two numbers of one figure, he will be able to perform the operation more readily, as follows: Add together 2, 4, 8, and 3. 2 4 Set down the figures under one another, 8 3 17 and say 3 and 8 are 11, 11 and 4 are 15, 15 and 2 are 17. SECTION II. Addition of a number of one figure to any number of two figures. Find the sum of 18 and 7. In Since 18 is I ten 8 units, if we add 7 units, we get 1 ten 15 units, or 2 tens 5 units, that is 25. the same way it may be shown that 28 and 7 are 35; 38 and 7...45; 68 and 7...75; 88 and 7...95, and so on. The pupil should practise exercises like these:-6 and 7 are 13, 16 and 7...23, 26 and 7...33; 9 and 8 are 17, 19 and 8...27, 29 and 8...37, 59 and 8...67, 79 and 8...87, and so on. SECTION III. Addition of any numbers whatever. Rule. Place the numbers under one another in such a manner that units may stand under units, tens under tens, hundreds under hundreds, and so on, and draw a horizontal line under the last row of figures. Add up the figures in the first column on the right hand, set down the units figure in their sum, and carry the tens (if any) to the next column; proceed in the same manner till the last column is added, when both the units and tens (if any) must be set down. Proof. The accuracy of the addition may be tested by adding the columns downwards as well as upwards. Examples.-Add together 5387, 4639, 584, 6357, 78. 5387 4639 584 6357 78 17045 Placing the numbers under one another, according to the rule, we add the figures in the units column thus-8 and 7 are 15, and 4 are 19, and 9 are 28, and 7 are 35, that is, 35 units, or 3 tens 5 units; set the 5 under the units figures, and carry the 3 tens to the column of tens. Beginning with the 3 carried, we say 3 and 7 are 10, and 5 are 15, and 8 are 23, and 3 are 26, and 8 are 34, that is, 34 tens, or 3 hundreds 4 tens ; set the 4 tens under the tens' figures, and carry the 3 hundreds to the hundreds' column; adding this in the same manner, we find the sum to be 20, that is 20 hundreds, or 2 thousands o hundreds, put o in the hundreds' place (because if we do not the next figure will be taken for hundreds instead of thousands), and carry 2 thousands to the thousands' line; proceeding as before, we find the sum to be 17, that is, 17 thousands, and this being the last column, we set down 17. The following sign + is sometimes used to express the addition of two or more numbers, and is read plus, or more by. The words is equal to, or equals, are usually denoted by two parallel straight lines thus=. Hence 5+7=12 is read 5 plus 7 equals 12. B. (1) 10134 231 143 432 134 124 213 |