SECTION III.

ADDITION

54. Addition is the process of uniting two or more numbers to form one number.

The Terms used in Addition are Addends, or Parts, and Sum, or Amount.

55. The Addends, or Parts, are the numbers to be added.

56. The Sum, or Amount, is the result obtained by Addition.

57. Signs are characters used for abbreviating expres

sions.

58. The Sign of Addition is an erect cross called plus (+), and when placed between numbers signifies that they are to be added. Thus, 3 + 2 means that 3 and 2 are to be added, and is read "3 plus 2."

The term plus, Latin, signifies more, or added to.

59. The Sign of Equality is two short, horizontal, parallel lines (=), and when placed between numbers signifies that they are equal. Thus, 3 + 2 = 5 means that 3 and 2 are equal to 5, and is read "3 plus 2 equals 5.”

60. The Sign of Dollars is a capital S with two vertical marks across it ($), and when placed before a number expresses dollars. Thus, $120 means 120 dollars.

5 5 5 5 5 5 5 5 5 5 10 10 10 10 10 10 10 10 10 10

5 6 7 8 9 10 11 12 13 14 10 11 12 13 14 15 16 17 18 19

Oral Exercises

EXAMPLE.-James has two hats and John has 3. How many have both?

Solution.-Since 2 hats and 3 hats are 5 hats, they both have 5 hats.
Or, 2 hats and 3 hats are 5 hats. Therefore. they both have 5 hats.
Or, They both have 5 hats, because 2 hats and 3 hats are 5 hats.

1. Willie found 4 marbles and bought 7. How many had he then? and 4 are how many? 9 and 2?

2. Samuel has 5 walnuts and James gives him 4 more. How many has he then? How many are 5 and 4? 4 and 5? 2 and 2 and 5? 3 and 2 and 4? 1+4+4=? 1+3+5=? 2+2+2+3=?

3. Charles bought 7 almonds at one store and 10 at another. How many did he buy in all? 7+10=? 10 + 7 = ? 7 +5 +5 = ? 2 + 8 + 7 = ? 6+7+4=? 3+7+7=? 9+3+5=?

4. If a pound of sugar costs 9 cents and an orange 6 cents, what will both cost? 6 cents and 9 cents are how many cents?

5. Jennie's father paid 8 dollars for her muff, 7 dollars for her tippet. How much did he pay for both? 7+8=?

6. If a house has 7 windows in the front and 6 in the rear, how many windows has it? 6 + 7 = ? 4 + 2 + 5 +2 ?

7. Mary paid 8 cents for an inkstand and 5 cents for a pencil. How much did she pay for both? 5 cents + 8 cents

=

?

How many are

8. 10 men and 7 men? 13.5+2+3? | 18. 7 toys and 7 toys? 9.8 boys and 9 boys ? 14. 5+3+1? 19. 6 miles and 8 miles? 10. 6 girls and 8 girls? 15. 3+3+3? 20. 8 cups and 4 cups? 11.5 tops and 9 tops? 16. 4+4+4? 21. 7 cents and 5 cents? 12. 3 pins and 8 pins ? 17.5+5+5? 22. 6 figs and 5 figs?

23. How many are 8 chairs and 4 dollars?

We cannot add 8 chairs and 4 dollars. For 8 chairs + 4 dollars = neither 12 chairs nor 12 dollars. Hence,

62. Only abstract numbers, or like concrete numbers, can be added.

24. How many are 3 tens and 9 thousands?

We cannot add 3 tens and 9 thousands. For 3 tens + 9 thousands = neither 12 tens, nor 12 thousands. Hence,

63. Only like orders of units can be added.

Written Exercises+

CASE I.

64. When the sum of all the units of each order is less than 10.

EXAMPLE.-What is the sum of 11, 431, 2245, 3112?

Addends.

Amount.

11 = 431 =

SOLUTION.

1 ten 1 one

4 hundreds 3 tens 1 one 2245 2 thousands 2 hundreds 4 tens 5 ones 3112 = 3 thousands 1 hundred 1 ten 2 ones 57995 thousands 7 hundreds 9 tens 9 ones

EXPLANATION.-Since only like orders can be added, it is most convenient to write like orders in the same column.

We first add the ones, 1, 1, 5, and 2, and find their sum to be 9, which we write in the ones' order of the amount.

We then add the tens, 1, 3, 4, and 1, and find their sum to be 9, which we write in the tens' order of the amount.

We then add the hundreds, 4, 2, and 1, and find their sum to be 7, which we write in the hundreds' order of the amount.

We then add the thousands, 2 and 3, and find their sum to be 5, which we write in the thousands' order of the amount. The result, 5799, is the sum required.

Ans. 9986.

8. Add 6404, 2213, and 1231.

Ans. 89.

Ans. 7976.

Ans. 9667.

9. Add 3472, 4513, 1001, and 1000. 10. Add 10, 12, 21, 32, 11, and 3. 11. Add 1321, 2312, 1241, and 3102. 12. Add 3131, 2112, 3421, and 1003. 13. Add 10102, 4030, 634, 11, and 2. 14. John gave 10 cents for a spelling-book, 12 cents for a writing-book, 15 cents for a slate, 20 cents for pens and ink, and 31 cents for an Arithmetic. How much did he give for all? Ans. 88 cents.

Ans. 14779.

15. One horse cost 120 dollars, another 115 dollars, one harness 31 dollars, the other 30 dollars, and the carriage 200 dollars. How much did all cost? Ans. 496 dollars. 16. Gave 3216 dollars for land, 2150 for a house, 1502 for stock, and 2121 for a barn. How much did all cost? Ans. 8989 dollars.