SECTION II. ADDITION. 36. Illustrative Example. How many books are 5 books, 3 books, and 2 books? SOLUTION. The numbers 5, 3, and 2 together make 10. 37. Putting numbers together to find what number they make is adding them. 38. The numbers to be put together are addends. The number found by adding two or more numbers is their sum or amount. 39. Addition is the process of putting two or more numbers together to find their sum or amount. 40. Only numbers of the same kind, name, or denomination can be added together, as apples with apples, pounds with pounds, units with units, tens with tens, hundreds with hundreds, etc. indicated by 41. The operations of arithmetic signs. The sign of addition is an upright cross, +. It is read "and" or "plus." The sign indicates equality, and is read "equals" or "is equal to." The expression 5+3+2 = 10 means that 5 and 3 and 2, added, make 10; it is read "5 plus 3 plus 2 equals 10." What is the sum in the example given above? What are the addends? Define addition. Oral Exercises in Addition. 42. I. Add each pair of numbers expressed in the columns a, b, c, etc., on the opposite page, till you can give the sums rapidly at sight. II. Add each pair expressed in lines m, n, o, etc. III. Count to thirty or more, s. By twos, beginning with 2; with 1. t. By threes, beginning with 2. Count to sixty or more, u. By fours, beginning with 3; v. By fives, beginning with 4; w. By sixes, beginning with 5; with 2. with 3; with 2; with 1. with 4. Count to a hundred or more, IV. Add the following as expressed in columns a, b, c, etc., counting from below upwaru and naming results only; thus, in column a, say 5, 7, 10, 12. To test the accuracy of the adding, add from above downwards. a b C d e f m 2+ 3+ 4+2+3+4 n 3+ 4+ 5+3+4+5 o 2+4+6+2+4+6 p 5 + 6 + 5+ 6+5+6 g h i j k q 6+ 7+6+7+6+7 r 6 + 5 + 6 + 5+ 6+ 5 87 +6 +9 +7+6+9 t 9 + 7+ 8+9+7+8 V. Add the above by lines from left to right. FR. AR. -2 Add the following by columns and by lines as indicated. a b C d e k 27+5+7+5+7+5 138+7+8+7+8+7 m 55+8+5+8+5+8 n 49 +6+9+6+9+6 o 26+7+5+8+9+8 p 35+8+9+7+5+6 q 46+5+4+6+8+7 f g h i j r 37+9+5+7+9+3 829+6+8+9+6+8 t 54 +8 +7+4+8+7 u 68+9+7+8+9+8 v 57+4+6+5+7+5 w 69+2+7+4+9+8 x 45+7+6+5+8+9 VI. Add the following by columns upward and downward; thus, in column a, say "20, 50, 60, 80, 100, 110.” VII. Add by lines from left to right, and from right to left. VIII. Add the above again and disregard the zeros till after adding; thus, in column a, say “2, 5, 6, 8, 10, 11 tens, or 110"; in column f, say "3, 7, 9, 12, 13, 15 hundreds, or 1500." IX. v. How many times does the hammer of a common clock strike from one to ten o'clock inclusive? w. A maid counting the silver of a house, found that there were 22 teaspoons, 12 coffee spoons, 6 table spoons, 9 dessert spoons, 4 salt spoons and 2 sugar spoons, and that 2 teaspoons were missing. What number of spoons belonged to the house? Examples for Written Work. 43. Illustrative Example. What is the sum of 824, 571, 278, and 636 ? WRITTEN WORK. 824 571 278 636 Sum, 2309 For convenience, the numbers are written so that units of the same order shall be expressed in the same column, and a line is drawn beneath. Beginning with the units to add (thus, 6, 14, 15, 19), there are 19 units = 1 ten and 9 units. The 9 is written in the units' place, and the 1 ten is kept to add with the tens. Adding the tens (thus, 1, 4, 11, 18, 20), there are 20 tens = 2 hundreds and no tens. A zero is written in the tens' place, and the 2 hundreds are kept to add with the hundreds. Adding next the hundreds, the sum of all the numbers is found to be 2309. Ans. 2309. Keeping a number to add with the numbers expressed in the next column is called carrying. In working examples, use as few words as possible; thus, in the illustrative example, say merely "6, 14, 15, 19;* 1, 4, 11, 18, 20; 2, 8, 10, 15, 23; sum, 2309." Add the following by columns; keep the answers and find their sum. 8. 274 +132 +972 + 34+ 346 + 6079 + 8460 =? 9. 206+618 + 980 + 800 +682 + 10. 87+ 416+ 592 =? 11. 428 +53 + 89 +675 + 798 + 5164 + 9087 =? ? + ? + ? + ? + ? + ? + ? =? Add the above numbers by lines; keep the answers and find their sum. How should the sum compare with the sum of the answers found in adding the numbers by columns? * Do not stop to say "write 9, carry 1," but do it. Add the following numbers by columns; also add them by lines. 19. 3072 +5932 + 4320 + 1243 + 3201 + 9876=? 23. ADDITION OF DECIMALS. 44. Illustrative Example. What is the sum of 564.18, $29.45, 207.136, 81.95, and 165.029 ? WRITTEN WORK. 564.18 329.45 207.136 81.95 165.029 1347.745 The numbers are written so that units of the same order shall be expressed in the same column. The adding begins with the units of the lowest order, and proceeds briefly, thus: Thousandths, 9, 15; write 5, carry 1. Hundredths, 1, 3, 8, 11, 16, 24; write 4, carry 2. Tenths, 2, 11, 12, 16, 17; write 7, carry 1, etc. Ans. 1347.745. Add the following by columns and by lines. 25. 26. 27. 28. 0.045 =? 29. 321.06 + 508.7 + 0.675 + 30. 31. 8.19 =? 32. 407.076+ 9.58 +119.04 + 69.909=? 33. ? + ? + ? + ? =? |