ADDITION. 29. 1. If one man gives me 5 pears and another gives me 4 pears, how many pears do I have? 2. John gives to William 7 marbles, to James 4, and to Edward 5; how many marbles does John give away? 30. The sum or amount of two or more numbers is a number which contains the same number of units as the two or more numbers together; thus, 7 is the sum of 3 and 4, because there are just as many units in 7 as in 3 and 4 together; for a like reason 11 days is the sum of 2 days, 4 days, and 5 days. 31. Only numbers of the same kind can be added; thus, 3 books and 4 books are 7 books; but 3 hats and 4 books are neither 7 hats nor 7 books. 32. Addition is the process of finding the sum of two or more numbers of the same kind. 33. A Sign is a mark which indicates an operation to be performed, or which is used to shorten some expression. 34. The sign of dollars is written thus, $; thus, $2 represents two dollars; $10, ten dollars, etc. 35. The sign of equality,=, signifies that the quantities between which it stands are equal to each other; thus, $1 = 100 cents, or, one dollar equals one hundred cents. 36. The sign of addition, +, called plus, denotes that the quantities between which it stands are to be added together; thus, 325, that is, three plus two equals five, or, three and two are five. 37. Oral Exercises. 3. James paid $4 for a pair of skates, $3 for a sled, and $1 for a knife; what did he pay for all? 4. What is the sum of $6 and $3? $5+$3+$7=? 5. What is the sum of 4+6+2+3? 3+5+8+ 2 = ? 6. I bought 7 liters of strawberries of one man, 4 liters of another, and 5 of another; how many liters did I buy? 7. John had 8 cents, Peter 9, and Henry 7; how many cents have the three boys? 11. Add to fifty by twos, beginning with 0; with 1. 12. Add to fifty by threes, beginning with 0; with 1; with 2. 13. Add to sixty by fours, beginning with 0; with 1; with 2, with 3. 14. Add to sixty by fives, beginning with 0; with 1; with 2; with 3; with 4. 15. Add to sixty by sixes, beginning with 0; with 1; with 2; with 3; with 4; with 5. 16. Add to seventy by sevens, beginning with 0; with 1; with 2; with 3; with 4; with 5; with 6. 17. Add to eighty by eights, beginning with 0; with 1; with 2; with 3; with 4; with 5; with 6; with 7. 18. Add to ninety by nines, beginning with 0; with 1; with 2; with 3; with 4; with 5; with 6; with 7; with 8. 19. I paid 12 cents for butts for a screen door, 4 cents for screws, 6 cents for a knob, and 3 cents for a hasp; what did the trimmings cost me? 20. For my breakfast I bought 5 cents' worth of crackers, 3 cents' worth of berries, and 4 cents' worth of milk; what did my breakfast cost me? 21. Bought 2 quarts vinegar for 24 cents, 1 box ginger for 12 cents, a pound of cream tartar for 35 cents, 6 eggs for 12 cents; how many cents must be paid to settle the bill? 22. Find the sum of 24, 17, 23, and 13. Add by 10's; thus, 24 and 1724 + 10 +7; say 24, 34, 41. 41 and 23=41+10+10+3; say 41, 51, 61, 64; or, say 41, 61, 64, adding the 20 at once. 64 and 13 64+10+3; say 64, 74, 77. To add the numbers given, then, say 24, 34, 41 (looking at 17), 61, 64 (lookAns. 77. ing at 23), 74, 77 (looking at 13). 23. Find the sum of 43, 18, 27, and 35. 24. On my bill I find 6 lemons 15 cents, 7 pounds of beef 98 cents, a cabbage 10 cents, turnips 5 cents, a half peck of beans 15 cents; for these how much do I owe? Begin with the 98, the largest number; thus, 98, 108, 113, etc. 25. 83+13 + 17 + 24 =? 26. 77+ 16 + 12 + 15 =? 27. 125 +11 +19 +21=? · 38. Exercises for Written Work. 28. A manufacturer sold 125 meters of cloth to one merchant, 342 to another, and 231 to another; how many meters did he sell in all? OPERATION. 125 342 231 Sum, 698 As we add units to units, tens to tens, etc., we write the units under the units, the tens under the tens, and the hundreds under the hundreds. Adding the units, thus, 1 (and 2 are) 3, (and 5 are) 8, we write the 8 units under the units' column; then adding the tens, thus, 3 (and 4 are) 7, (and 2 are) 9, we write the 9 tens under the tens' column, and so proceed, till all the columns are added. In adding it is better not to name the numbers we are adding; thus, in Ex. 28, omit the words enclosed in parentheses in the explanation above. 37. What is the sum of 4123, 1331, and 2211? 38. What is the sum of 1123, 2112, 3201, and 2213 ? 39. A gentleman paid $125 for a horse, $ 231 for a carriage, and $32 for a harness; what did he pay for all? 40. Add together 27, 93, and 145. OPERATION. 27. 93 145 Arranging the numbers as before, we add the units, thus, 5, 8, 15 units, or, 1 ten 5 units. The 5 units we write under the units' column, and add the 1 ten to the tens in the second column, thus, 1, 5, 14, 16 tens, or 1 hundred and 6 tens. The 6 tens we write under the tens' column, and add the 1 hundred to the hundreds in the third column, thus, 1, 2 hundreds, which we write under the hundreds' column. Ans. 265 41. What is the sum of 37.43, 567.8, 8.148, 917.767, and 0.09 ? OPERATION. 37.43 567.8 Ans. 1531.235 Hence, Writing the numbers with units of the same order in the same column, we add the units of the right-hand column, thus, 7, 15; writing the 5 of the 15 in its place, we add the 1 to the next column, thus, 1, 10, 16, 20, 23; writing the 3 of 23 in its place, we add the 2 to the next column, thus, 2, 9, 10, 18, 22; and so on, precisely as in Ex. 40, remembering also to place the decimal point directly under the points in the numbers added. 39. To add numbers, Rule. Write the numbers in order, units under units, tenths under tenths, etc., and draw a line beneath. Add together the figures in the right-hand column, and write the units of this sum directly under this column, and the tens of this sum, if there are any, add to the units of the next column. Thus proceed till all the columns are added, and place the decimal point directly under the points in the numbers added. 40. PROOF. Add the columns in the opposite direction, and if the work is right, the two sums will be alike. NOTE 1. By this process, we combine the numbers differently, and hence are likely to detect any mistake which may have been made in the first addition. (42.) 37684 48297 68746 94852 Sum, 249579 Proof, 249579 In adding the first column upward we say, 2, 8, 15, 19; but in adding downward, we say, 4, 11, 17, 19; thus obtaining the same result, but by different combinations. If we do not obtain the same result by the two methods, one operation or the other is wrong, perhaps both, and the work must be carefully performed again. |