35. To write numbers in figures.

1. Let it be required to write in figures, seven million six hundred ninety-three thousand two hundred four.

Writing the 7 millions as the only order of the third period, the 693 thousands as the orders of the second period, and the 204 as the orders of the first period, we have 7,693,204. Hence, the following

RULE. Beginning with the highest period to be expressed, write the figures belonging to each period, in their orders, observing to mark the omission of any order of units with a cipher.

Examples.

Write in figures the following numbers:

2. 8 tens 7 units.

3. 3 units of the third order and 1 of the first.

4. One hundred twenty-five.

5. 7 hundreds nine tens 6 units.

6. 8 units of the second order and 9 of the first.

7. Nine hundred ninety-seven.

8. Five thousand sixty-two.

9. Fifty-five thousand five hundred. 10. One hundred six thousand.

Ans. 87.

Ans. 301.

11. 90 thousands nine hundreds.

Ans. 90,900

12. 100 thousands 7 hundreds 6 tens 4 units.

13. One hundred thousand four hundred fifteen.

14. Thirty-six thousand forty-six.

15 One million one hundred thousand one hundred.

16. One hundred fifty-one millions.

17. 3 billions 4 millions 14 thousands 4 hundreds 5 tens units.

Ans. 3,004,014,45€

18. Sixteen trillions seven hundred forty-one billions two hundred twenty-three millions one hundred seventy-eight thousand.

Repeat the Rule.

ADDITION.

36. 1. Arthur has 4 books and his sister has 3; how many have both together?

SOLUTION. They have, together, as many books as are equal to 4 books and 3 books, which are 7 books. Therefore, they both together Lave 7 books.

2. Paid 8 cents for a pencil and 2 cents for a pen-holder; how much did I pay for the whole?

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

4. John has 2 apples, Edward 7, and Henry 9; how have they together?

5. How many are 3 and 1 and 8? 2 and 0 and 6?

many

6. In a yard are 10 peach trees, 5 apple trees, and 4 plum trees; how many trees are there in all?

The preceding operations are called ADDITION. Hence,

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

The SUM or AMOUNT is the result of the addition; and contains as many units as there are in all the numbers added.

38. A SIGN is a mark used to denote an operation to be performed, or to shorten an expression.

The SIGN OF ADDITION is an erect cross, +, called plus. Thus, 3+2, 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 are equal to. Thus, 3+2= 5, is read, three plus two are equal to five.

What is Addition? The Sum or Amount? A Sign? The Sign of Ad dition? The Sign of Equality?

39. The process of Addition is based upon the following

PRINCIPLES.

1. Like numbers, and units of the same order, alone can be added.

Thus,

Dollars and dollars can be added, but not dollars and days; also, units and units, tens and tens; but not units and tens.

Repeat the column 1 and 1. 2 and 1. 3 and 1. 4 and 1, etc. What is the first Principle?

2. The sum of two or more numbers is the same in whatever order they are added. Thus,

The sum of 2, 5, and 3 is 10, and the sum of 5, 3, and 2, or of 3, 2, and 5, is 10.

3. The sum and the numbers added must be like numbers. Thus,

The sum of 4 dollars and 6 dollars is 10 dollars, not 10 pounds.

40. To add numbers.

1. Let it be required to add 236, 541, and 102.

OPERATION.

236

541

102

Sum, 879

9 units, or 879.

OPERATION.

For convenience, we write the given numbers so that all the figures of the same order stand in the same column, and begin with units to add.

2, 1, and 6 units are 9 units, which we write. 0, 4, and 3 tens are 7 tens, which we write. 1, 5, and 2 hundreds are 8 hundreds, which we write. Therefore, the sum is 8 hundreds, 7 tens, and

2. Let it be required to find the sum of 595, 361, and 723. For convenience, we write, as before, the figures of the same order in the same column, and begin with units to add.

595

361

723

Sum, 1679

3, 1, and 5 units are 9 units, which we write. 2, 6, and 9 tens are 17 tens, or 1 hundred and 7 tens; we write the 7 tens and add the 1 hundred in with hundreds.

1, 7, 3, and 5 hundreds are 16 hundreds, or, 1 thousand and 6 hundreds, which we write.

Therefore, the sum is 1 thousand, 6 hundreds, 7 tens, and 9 units, or

1679.

In practice, it is sufficient to name only results. Thus, in the operation, we may say: three, four, nine,—write 9; two, eight, seventeen, — write 7 and add 1 with next column; eight, eleven, sixteen, write 16; answer, 1679.

What is the second Principle? The third ?

RULE.

Write the numbers to be added so that figures of

the same order shall stand in the same column.

Begin at the right, add the numbers expressed by the figures of each column separately, and write the sum underneath, if less than ten of the order added.

If, however, the sum is ten or more, write the right-hand figure underneath, and add the number expressed by the other figure or figures with the numbers of the next column.

Write the whole sum of the last column.

PROOF. Add the numbers a second time, in the same manner as at the first, except in an opposite direction, and, if the result agrees with that first obtained, the work is supposed to be correct. Or,

Separate the given numbers into parts; add each of the parts, and then add their sums; and, if the result agrees with that first obtained, the work is supposed to be correct.

The test, by either proof, consists in doing the work twice, in a different manner.

Repeat the Rule. What is the first Proof? The second Proof?