The third period is 7 millions, the second period is 693 thousands, the first period is 254 units; therefore, the whole reads, seven million six hundred ninety-three thousand two hundred fifty-four. Hence, the following

Rule.-Beginning at the units' order, point off the given expression into as many periods as possible, of three figures each.

Then, begin at the left and read each period, giving after each, excepting the last, the name of the period.

What is Numeration?

At which hand do you begin to point off numbers? At which to read? Recite the Rule. Why is the name of the units' period not given in reading figures? Ans. Because the name is understood.

38. 1. If James has 4 books and John 2, how many books have both of them?

2. Four trees and 3 trees are how many trees? How many are 4 and 3?

3. If a house has 5 windows in the front, and in the side 6, how many windows has it both in the front and in the side?

How many are 5 and 6?

39. Addition is the process of finding a number equal to two or more given numbers of the same kind.

The SUM is the number which is equal to the numbers added.

Thus,

The sum of two cents and 3 cents is 5 cents.

40. A Sign is a mark used to shorten an expression, or to indicate a process.

What is Addition?

The Sum or Amount? What is a Solution? Ans. The answering of a question, or giving in order the steps required to obtain its answer.

The Sign of Addition is an erect cross, +, and is

called plus. Thus,

32, which is read three plus two, denotes that 3 and 2 are to be added.

The Sign of Equality is two short parallel horizontal lines, and is read equals, or equal to. 325, is read, three plus two

Thus,

are equal to five.

8

9

5

66 10

9

66

10 6 66

11

7

66

10

66

11 7 66

12

9

8

66

12

REVIEW. - What is Notation? (32.) Numeration? (36.) What is the Rule for writing numbers? (35.) For reading numbers? (37.)

44. How many are 11 and 7? 21 and 7? 51 and 7?

71 and 7? 12 and 3? 32 and 3?

45. How many are 16 and 2? 66 and 5? 96 and 5? 17 and 3? 46. How many are 18 and 7? 98 and 7? 14 and 7? 27 and 7?

83 and 3?

46 and 2? 46 and 5?

37 and 3?

28 and 7? 68 and 7?

47. How many are 19 and 8? 29 and 8? 69 and 8? 89 and 9? 10 and 9? 20 and 9? 80 and 9?

MENTAL EXERCISES.

1. John has 4 apples, Arthur 3, and Henry 2; how many have they in all?

SOLUTION. They have the sum of 4 apples, 3 apples, and 2 apples; 4 and 3 are 7, and 2 are 9. Therefore, they have in all 9 apples.

2. Paid for paper eight cents, and for pencils 6; how much was paid for the whole?

3. James caught 7 fishes, Ernest 5, and Albert 6; how many were caught by them all?

4. Gave 9 dollars for coal, and 11 dollars for wood; how many dollars were given for both?

5. If a writing-book costs 10 cents, a pen 5 cents, and a slate 9 cents, how much do they all cost?

6. A clothier sold a hat for 5 dollars, a vest for 9, and a coat for as much as he sold both the hat and vest for; for how much was the coat sold?

7. Jane has 5 books at school, 7 at home, and has loaned 6; how many has she in all?

8. In one pasture are 10 sheep, in another 7, and in a third 8; how many are there in all?

9. A farmer had 27 cows and bought 8 more; how many had he then?

REVIEW.-What is the method of expressing numbers by figures called? (32.)