EXPLANATION -These Tables are designed for a brief exercise at the beginning or close of the daily recitation, and should be dwelt upon until the pupil is familiar with the various combinations. Let the pupil recite the table assigned to him, as the signs indicate; thus, in No. 1, 4 and 8 are 7, 5 and 6 are 11, etc.; in No. 16, 18 less 4 are 9, etc.; in No. 81, 6 times 8 are 48, etc.; in No. 46, 4 in 36, 9 times, eto 8 22 5 17 16 -8 24 11 12 9 18 7 23 - 16285 - The tables, may be profitably used in many ways. The columns may be added upward or downward, or substituting + for, X, and, add across the page. Substituting for, the table for division becomes a table for subtraction. By dividing the dividend of one example by the divisor of another, mixed numbers may be obtained; thus, in Nos. 46 and 47, say 4 in 25, 5 in 36, 7 in 48, etc. WRITTEN ARITHMETIC. 1. On page 26 the pupil nas learned the names and meaning of the ten Arabic figures, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; and on page 27 he has learned the names and uses of the signs, $, = +, 2. The learner has also doubtless observed that the value of a figure depends not only on the figure itself, but also on the place the figure occupies; for example, 4, standing alone, means four units, or ones; but when the 4 is made to occupy the second place, by putting 0 or any other figure on the right of it, it becomes four tens; thus, 40 equals four tens, or forty; 46 equals four tens plus six, that is, forty-six, etc. Again, when two figures are at the right of 4, the 4 becomes four hundreds, which equals ten times four tens; that is, each remove of a figure one place toward the left makes its value ten times as much as it was before. This will be seen in the following Table: = = = Two hundred and twenty-two thousand, two hundred and twenty-two. Five thousand four hundred and ninety-six. 1. Forty-seven. 2. Sixty. 3. Two hundred and seventy-nine. 4. Five hundred and eight. 5. Three thousand, five hundred and sixty-two. 6. Eight thousand and two hundred. 7. Sixty-two thousand, five hundred and twenty. 8. One hundred and six thousand, two hundred and four. 9. Four hundred thousand, four hundred and thirteen. ADDITION. 5. BY ADDITION we find how many units there are in two or more numbers taken together. The result of the addition is called the SUM, or AMOUNT. 6. To add when the amount of each column is less than ten. Ex. 1. A farmer sold 125 bushels of corn, 342 bushels of oats, and 231 bushels of wheat; how many bushels of grain did he sell? Ans. 698. OPERATION. 125 231 Having set the numbers so that units stand 342 under units, tens under tens, etc., add the units; thus, 1 and 2 are 3, and 5 are 8, and set the 8 Sum, 698 under the column of units. Then add the tens; thus, 3 and 4 are 7, and 2 are 9, and set the 9 under the column of tens, and so proceed till all the columns are added. In like manner add the following examples: 16. A man paid $112 for a horse, $235 for a chaise, and $41 for a harness; what did he pay for all? 17. A gardener has 231 apple trees, 124 pear trees, 322 peach trees, and 200 cherry trees; how many trees has he? 18. Add together 205, 342, 120, and 212. 19. Add together 134, 213, 401, and 141. 20. What is the sum of 1231, 3214, and 4323? 21. What is the sum of 5100, 1424, and 2432 ? *. To add when the amount of any column is ten or more. 22. A man bought 4 farms. The first contained 345 acres, the second 244 acres, the third 346 acres, and the fourth 638 acres; how many acres were there in the 4 farms? OPERATION. 244 346 638 We find the sum of the units to be 23, or 2 tens and 3 units. We write the 3 units under the column of units, and add the 2 tens to the tens in the next column, making 17 tens, or 1 hundred and 7 tens. The 7 tens are written in the place of tens, and the 1 hundred, added to the hundreds in the example, giving 15 hundreds, or 1 thousand and 5 hundreds; and when these figures are written in their respective places, the example is solved. Sum, 1573 8. In the same manner add the numbers in the following short columns; also add across the page, as suggested by the signs. 23. 42363648 + 7264 + 8324 + 3663 +2547 3826 27. 23561427 + 3240 + 5124 + 6312 + 2436 5430 5376 6004 8241 |