24. Add by 2's and 3's alternately from 1 to 31. OPERATION.—1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31. 25. Add by 2's and 4's alternately from 1 to 49. 26. Add by 3's and 4's alternately from 0 to 56. 27. Add by 2's and 5's alternately from 4 to 60. 28. Add by 3's and 5's alternately from 7 to 63. DEFINITIONS AND PRINCIPLES. 60. Addition is the process of finding a number equivalent to two or more numbers. 61. The Sum or Amount is the number obtained by addition. 62. The Sign of Addition is +. It is read plus, and signifies more; thus, 5 + 6 is read, 5 plus 6, and means that 5 and 6 are to be added. 63. The Sign of Equality is =. It is read equals, or equal to; thus, 5 + 6 = 11, is read 5 plus 6 equals 11. It may be read 5 and 6 are 11. 64. An Equation is an expression of equality between two numbers or sets of numbers. Thus, 6 + 4 = 10, is an equation, and is read 6 plus 4 equals 10, and means that the sum of 6 and 4 is equal to 10. 6 + 4 is the first member of the equation, and 10 is the second member; and 6, 4, and 10 are the terms of the equation. 65. Name the members and the terms of each of the following equations. 1. 9+12=21 3. 26935 5. 14+40=44+10 2. 14+10=24 | 4. 44+12=56 6. 18+20=31+ 7 66. PRINCIPLE.-Only like numbers and units of the same order can be added. EXERCISES. 67. The teacher should read the first member of the equation, and the pupil be required, as promptly as possible, to give the second member. The expression"?" is read equals how many, or what. 68. When the sum of the units of each order is less than 10. 1. What is the sum of 421, 44, 303, and 230 ? OPERATION. 421 44 303 230 998 Sum. ANALYSIS. Arrange the numbers so that the units of the same order stand in the same column. Begin with the lowest order of units, and add each column separately; and instead of saying, 3 units and 4 units are 7 units, and 1 unit are 8 units, pronounce the successive results only; thus, 3, 7, 8, the sum of the units, which write in the units' place. Next, 3, 7, 9, the sum of the tens, which write in the tens' place. Lastly, 2, 5, 9, the sum of the hundreds, which write in the hundreds' piace. Hence the sum is 998. PROOF.-Add the columns in the reversed direction. If the two results agree, the work is probably correct, 6. I paid 3104 dollars for a house, 450 dollars for repairs, and 234 dollars for painting. What was the whole cost? 69. The Sign of Dollars is $. It is read dollars. Thus, $35 is read 35 dollars; $9 is read 9 dollars. 70. When dollars and cents are written, a period or point (.) is placed before the cents, or between the dollars and cents. Thus, $7.25 is read 7 dollars and 25 cents. 71. Since 100 cents make $1.00, cents always occupy two places, and never more than two. 72. If the number of cents is less than 10 and expressed by a single figure, a cipher must occupy the first place at the right of the point. Thus, 3 dollars 6 cents are written $3.06; 1 dollar 5 cents are written $1.05. 73. When cents alone are written, and their number is less than 100, either write the word cents after the number, or place the dollar sign and the point before the number. Thus, 75 cents may be expressed, 8.75. 74. In arranging for addition, dollars should be written under dollars, and cents under cents, in such order that the points stand in a vertical line. The sign $, and the point (.) should never be omitted. 75. Read the following equations: 4. 5. 1. $12. + $8. = $20. 4. Seventy-eight cents. 9. 69 cents; 23 cents. 5. Six dollars and sixteen cents. 10. 10 cents; 6 cents. The teacher may exercise the class orally, by dictating rapidly, but distinctly, similar examples. Thus, Sign, five, three? The prompt response should be, "Fifty-three dollars" ($53). Ques. Sign, point, seven, four? Ans. Seventy-four cents ($.74). Ques. Sign, point, naught, eight? Ans. Eight cents ($.08), etc. Also, the converse; thus, Ques. "Forty-five dollars" ($45)? Ans. Sign, four, five. Ques. Fifty-six cents ($.56)? Ans. Sign, point, five, six. Ques. Nine dollars seven cents ($9.07)? Ans. Sign, nine, point, naught, seven; etc. 5. What is the sum of $.25, $3.31, $14.02, and $21. 6. What is the sum of ten dollars and twenty cents, four dollars and fifteen cents, forty-three cents, and thirteen dollars? 7. Bought a horse for $154, and sold him for $35.75 more than he cost. For how much did I sell him? 8. A lady paid 12 cents for a fan, two dollars for a pair of gloves, and 42 cents for a collar. How much did she pay for all? dollars for a scarf, 3 dollars and 25 It is not the design to teach here, the principles and reductions of Decimal Currency, fully taught in another place, but to give a few hints and illustrations, to enable the teacher, by oral instruction and simple written exercises, to make the pupil familiar with the use of decimal currency in common business matters. ORAL EXERCISES. 78. 1. How many are 7 and 6? 13 and 6? 19 and 6? 25 and 6? 31 and 6? 42 and 6? 2. How many are 9 and 7? 16 and 7? 23 and Y? |