126 NOTATION AND NUMERATION. 58. PRELIMINARY DEFINITIONS. SYNOPSIS FOR REVIEW. 1. Arithmetic. 2. A Unit. 3. A Number. 4. An Integral Number. 5. Unit of a Number. 6. A Concrete Number. 7. An Abstract Number. 8. Like Numbers. 9. Unlike Numbers. 10. A Scale. 11. A Uniform Scale. 12. A Varying Scale. 13. A Decimal Scale. 59. 1. A man gave 5 dollars for a hat, and 9 dollars for a vest. How many dollars did he pay for both? 2. How many miles are 4 miles and 12 miles? 3. How many are 6 men and 14 men? 15 and 7? 4. How many are 14 and 5? 29 and 5? 24 and 5? 21 and 6? 27 and 6? 7 and 19? 7 and 26? 5. How many are 15 and 6? 6. How many are 7 and 12? 7. What kind of numbers are 9 pounds and 14 pounds? 8. Can 9 balls and 12 books be added? Why not? 9. Can 7 rods and 10 rods be added? Why? 10. How many are 4, 5, and 7? 5, 7, and 4? 4, 7, and 5? 11. In a shop are 15 men, 8 boys, and 6 girls at work. How many persons are at work in the shop? 12. I gave 7 cents to one boy, 9 to another, and 6 to another. How many cents did I give to all? 13. Add by 2's from 1 to 31. OPERATION.-1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31. 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. 3. 26+ 9=35 5. 14+40-44 +10 6. 18+20=31+ 7 4. 44+12=56 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. 16 ADDITION. WRITTEN EXERCISES. 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 units 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' place. 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. |