60. 1. Find the sum of 284+8725+7643. PROCESS 284 8725 7643 16652 ANALYSIS. Write the numbers to be added so that fig. ures of the same order shall be in the same column. Add the figures in the column of units; write the unit figure of the sum under the column of units, and reserve the tens to be added to the column of tens. So proceed, column by column, writing the sum of the highest column in its proper place. · Name results only, thus, in adding column of units, say, 3, 8, 12; in adding column of tens, say, 5, 7, 21, etc. Find the sum in each of the following examples: 2. 375+896+6748+8496+9987+4876. 3. 18924+6768+375+4967+84969+56. 61. 1. Find the sum of 84.25+1.379+.8+.006. PROCESS. 84.25 1.379 .8 .006 86.435 ANALYSIS. Write as before, placing figures of the same order in the same column. The decimal points will thus be in the same column. Add as before. Find the sum in each of the following examples: 3. 9.45+.8475+.0098+.15+.5+5.+.75+29.834. 4. 368.492+3.756+.00768+2.49+.3974+50.092+.009. 62. The correctness of an addition may be tested in various ways, such as the following : 1. Add the columns in the opposite direction from that in which they were added at first. 2. If the columns are long, separate the example into two or more parts; find the sum of each part; then add these several sums. 3. Add two columns at once. ADDITION. TEACHERS' LA No.. 4. Find the sum of each column, or of two columns, separately. Write these sums in their proper places, or orders; then find the sum of these sums. Do this beginning with the right hand column, then with the left hand column. Find the sum of each of the following examples, and test accuracy of the addition by one or more of the methods given above. 2. 8469+9698+36745+67923+78469+87627. 3. 59764+76925+66784+664+6892+78925+6984. 4. 84.96+765.2+7.865+73.92+99.81+7.642+873.2. 5. 72.49+83.76+99.99+81.35+73.62+49.37+82.96+45 .64. 6. $45.32+$95.63+$435.+$735.67+$5.345+$78.465. PROBLEMS. 63. 1. The area in square miles of the six New England states is as follows: Maine 33040; N. H. 9305; Vt. 9565; Mass. 8315; Conn. 4990; R. I. 1250. Find their total area. 2. The area in square miles of the following States and territories of the U. S. is as follows: Idaho 84800; Wyoming 97890; Utah 84970; Arizona 113020; New Mexico 122580. Find their total area. 3. In the year 1882, the amount of corn raised in the U. S. was as follows, expressed in thousands of bushels. What was the total amount? N. E. States 6,376; Middle States, 78,586; Southern, 394,695; Western, 1,127,935; Pacific, 2,921; Nevada, Colorado, and territories, 6,512. 4. The ordinary receipts of the treasury of the U. S. for the fiscal year ending June 30, 1886, were: From customs, $192,905,023; from internal revenue, $116,805, 937; from direct taxes, $108,240; from sale of public lands, $5,630,999; miscellaneous, $20,989,528. What was the total revenue? 5. The pensions paid by the U. S. Government for the year ending June 30, 1887, were: Army, $49,376, 800; Navy, $834,576; War of 1812, $1,807,056; Mexi can war, $806,208. in pensions? What was the total amount paid SUMMARY. 64. The Sum, or Amount, of two or more numbers, is the number that contains exactly as many units as the given numbers. 65. Addition is a process of finding the sum of two or more numbers of the same kind. 66. Only like numbers can be added. Eight books and 4 books are 12 books; but 8 books and 4 knives are neither 12 books nor 12 knives. 67. Like numbers are said to have the same unit value. 68. The Sign of Addition is +, plus. 69. The Sign of Equality is = Equals. 70. Examples in Addition, to be used at the discretion of the teacher. Examples 1 to 26, each one line across the page. Examples 27 to 41, eight numbers in each example of the first two sections; ten in each, of the third section. CHAPTER III. SUBTRACTION. Article 71. 1. Count by 1's from 10 to 0. This is subtracting 1 from 10, then from 9, etc. 2. Count by 2's from 20 to 0. This is the subtraction of 2 from 20, then from 18 etc. 3. Count by 2's from 21 to 1. 4. Count by 3's from 30 to 0; from 29 to 2; from 28 to 1. 5. Subtract 4 from 48; then from 44, and so on till nothing remains. 6. Count by 5's from 60 to 0. 7. Count by 10's from 100 to 0; from 88 to 8. 8. Subtract 4 from every number between 7 and 15. 9. Subtract 5 from every number between 40 and 30. Practice should be given in the subtraction of 6, of 7, of 8, of 9, etc. 72. Since 6 units and 4 units are 10 units, 10 units less 6 units are 4 units; or, expressed briefly, 10—6=4, which is read, 10 minus 6 equals 4. In this example, 10 is the minuend, the number from which 6, the subtrahend, is subtracted; 4 is the difference of 10 and 6, or the remainder when 6 has been subtracted from 10. The sign, in 10-6, is called minus, and shows that the number following it is to be subtracted from the number preceding it. 73. Find the differences 1. 12-5. 2. 15-9. 3. 13-8. 5. 23-19. |