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RULE FOR NOTATION. I. Beginning at the left hand, write the figures belonging to the highest period.

II. Write the hundreds, tens, and units of each successive period in their order, placing a cipher wherever an order of units is omitted.


-I. Separate the number into periods of three figures each, commencing at the right hand. II. Beginning at the left hand, read each period separately, and give the name to each period, except the last, or period of units.

34. Until the pupils can write numbers readily, it may be well for them to write several periods of ciphers, point them off, and over each period write its name, and then write the given numbers underneath in their appropriate places.


Trillions. Billions. Millions. Thousands. Units.
000, 000, 000, 000, 000.


Express the following numbers by figures:
1. Four hundred thirty-six.

2. Seven thousand one hundred sixty-four.
3. Twenty-six thousand twenty-six.

4. Fourteen thousand two hundred eighty.

5. One hundred seventy-six thousand.
6. Four hundred fifty thousand thirty-nine.
7. Ninety-five million.

8. Four hundred thirty-three million eight thousand.
9. Nine hundred thousand ninety.

10. Ten million ten thousand ten hundred ten.

11. Sixty-one billion five million.

12. Five trillion eighty billion nine million one.

Point off, numerate, and read the following num

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26. Write five hundred sixty-three thousand four. 27. Write one million ninety-six thousand.

28. Numerate and read 9004082501.

29. Numerate and read 2584503962047.

30. A certain number contains 3 units of the seventh order, 6 of the fifth, 4 of the fourth, 1 of the third, 5 of the second, and 2 of the first; what is the number?

31. What orders of units are contained in the number 290648 ?

32. What orders of units are contained in the number 1037050?

33. What orders of units are contained in the number 23975630?

34. What orders of units are contained in the number 349765248?

35. What orders of units are contained in the number 987654321 ?

Numerate and read the following numbers:

44. 24318422. 52. 43567890.

36. 87641832.

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35. 1. Henry gave $5 for a vest, and $7 for a coat. What did he pay for both?

SOLUTION. He gave 5 dollars and 7 dollars, which are 12


2. A farmer sold a pig for $3, and a calf for $8. What did he receive for both?

3. A drover bought 5 sheep of one man, 9 of another, and 3 of another. How many did he buy in all?

4. How many are 2 and 6? 2 and 7? 2 and 9? 2 and 8? 2 and 10?

5. How many are 4 and 5? 4 and 8? 4 and 7? 4 and 9?

6. How many are 6 and 4? 6 and 6? 6 and 9? 6 and 7?

7. How many are 7 and 7? 7 and 6? 7 and 8? 7 and 10? 7 and 9?

8. How many are 5 and 4 and 6? 7 and 3 and 8? 6 and 9 and 5?

36. Addition is the process of uniting several numbers of the same kind into one equivalent number.

37. The Sum or Amount is the result obtained by the addition.

38. The sign, +, is called plus (generally read and), which signifies more. When placed between two numbers, it denotes that they are to be added.

Thus, 64, shows that 6 and 4 are to be added.

39. The sign, =, is called the sign of equality. When placed between two numbers, or sets of numbers, it signifies that they are equal to each other.

Thus, the expression 6 + 4 = 10, is read 6 plus 4 are equal to 10, or 6 and 4 are 10, and denotes that the numbers 6 and 4, taken together, equal the number 10.


40. When the amount of each column is less than 10.

1. A farmer sold some hay for 102 dollars, six cows for 162 dollars, and a horse for 125 dollars. What did he receive for all?

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SOLUTION. - We arrange the numbers so that units of like order shall stand in the same column. Then we add the columns separately, for convenience commencing at the right hand, and write each result under the column added. The sum of the units column is 9, the sum of the tens column is 8, the sum of the hundreds column is 3. The entire amount is 3 hundreds 8 tens and 9 units, or 389.

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6. What is the sum of 144, 321, and 232 ?

Ans. 697.

7. What is the amount of 122, 333, and 401 ? Ans. 856.

8. What is the sum of 42, 103, 321, and 32? Ans. 498. 9. A drover bought three droves of sheep. The first contained 230, the second 425, and the third 340. How many sheep did he buy in all ? Ans. 995.

41. When the amount of any column equals or exceeds 10.

1. A merchant pays 725 dollars a year for the rent of a store, 475 dollars for a clerk, and 367 dollars for other expenses. What is the amount of his expenses?




Or Units.




Sum of the units,

Sum of the tens,


Sum of the hundreds, 14

Total amount,



SOLUTION. Arranging the numbers as in 40, we first add the column of units, and find the sum to be 17 units, which is 1 ten and 7 units. We write the 7 units in the place of units, and the 1 ten in the place of tens. The sum of the figures in the column of tens is 15 tens, which is 1 hundred, and 5 tens. We write the 5 tens in the place of tens, and the 1 hundred in the place of hundreds. Next we add the column of hundreds, and find the sum to be 14 hundreds, which is 1 thousand and 4

We write the 4 hundreds in the place of hundreds, and 1 thousand in the place of thousands. Lastly, by uniting the sum of the units with the sums of the tens and hundreds, we find the total amount to be 1 thousand 5 hundreds 6 tens 7 units, or 1567.

This example may be performed by another method, which is the common one in practice. Thus:




367 1567

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SOLUTION. Arranging the numbers, as before, we add the first column and find the sum to be 17 units; writing the 7 units under the column of units, we add the 1 ten to the column of tens, and find the sum to be 16 tens; writing the 6 tens under the column of tens, we add the 1 hundred to the column of hundreds, and find the sum to be 15 hundreds; as this is the last column, we write down its amount, 15; and the whole amount Is 1567, as before.

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