ART. 14. The following table exhibits the English method of numeration, in which it will be observed that the figures are separated by commas into periods of six figures each. The first or right-hand period is regarded as units and thousands of units; the second, as millions and thousands of millions; and so on, six places being assigned to each period designated by a distinct

The value of the figures in the above table, expressed in words according to the English method, is, One hundred thirty-seven thousand eight hundred ninety trillions; seven hundred eleven thousand seven hundred sixteen billions; three hundred seventyone thousand seven hundred twelve millions; four hundred fiftysix thousand seven hundred eleven.

Although there is the same number of figures in the English and in the French table, yet it will be observed that in the French table we have the names of three periods other than in the English. It will also be observed that the variation commences after the ninth place, or the place of hundreds of millions. If, therefore, we would know the value of numbers

QUESTIONS. Art. 14. How many figures in each period in the English method of numeration? What orders are found in the English method that are not in the French? Give the names of the periods in the English Numeration Table, beginning with the period of units. Repeat the table, giving the names of all the orders or places. What is the value of the numbers in the table expressed in words? How do the figures in the English and French table compare as to numbers? How as to periods? Why is this difference? Has a million the same value reckoned by the French table as when reckoned by the English?

higher than hundreds of millions, when we see them written in words, or hear them read, we need to know whether they are expressed according to the French or the English method of numeration.

The English method of numeration is that generally used in Great Britain, and in the British Provinces.

ART. 15. To numerate and read numbers expressed by figures according to the English method, we have the following'

RULE. ·Begin at the right hand, and point off the figures into periods of six places each. Then, commencing at the left hand, read the figures of each period, adding the name of each period, excepting that of units.

EXERCISES IN ENGLISH NUMERATION.

The learner may read orally, or write in words, the following numbers:

1.

2.

3.

4.

125 5.

1063 6. 25842 7.

904357 8.

27306387903 531470983712 4230578032765038

716756378807370767086389706473

ART. 16. To write numbers in figures, according to the English method, we have the following

RULE. Begin at the left hand, and write in each successive order the figure belonging to it.

If any intervening order would otherwise be vacant, fill the place by a cipher.

EXERCISES IN ENGLISH NOTATION AND NUMERATION.

The learner may write in figures, and read, the following numbers:

1. Three hundred twenty-five thousand four hundred and twelve.

2. Two hundred fourteen thousand, one hundred sixty-five millions, seventy-eight thousand and fifty-six.

3. Forty-two billions, six hundred seventeen thousand thirtyone millions, forty-one thousand three hundred forty-two.

4. Two thousand eight billions, nine thousand eighty-two millions, seven hundred one thousand, nine hundred and eight.

QUESTIONS. Has the billion the same value as that by the French table? Why not? By which table has it the greater value? Where is the English method of numerating in use?-Art. 15. What is the rule for numerating and reading numbers by the English method? Art. 16. What is the rule for writing numbers according to the English method?

§ II. ADDITION.

MENTAL EXERCISES.

ART. 17. WHEN it is required to find a single number to express the sum of the units contained in several smaller numbers, the process is called Addition.

Ex. 1. James has 3 pears, and his younger brother has 4 ; how many have both?

-

ILLUSTRATION. To solve this question, the 3 pears and 4 pears must be added together; thus, 3 added to 4 makes 7. Therefore James and his brother have 7 pears.

QUESTION. Art. 17. What is the process called by which we find the sum of several numbers?

2. How many are 2 and 3?

2 and 5? 2 and 7? 2 and 9?

2 and 4? 2 and 2? 2 and 8? 2 and 6?

3 and 5?

3. How many are 3 and 3? 3 and 7? 3 and 9? 3 and 4? 3 and 6? 3 and 8? 3 and 3? 4. How many are 4 and 3? 4 and 5? 4 and 8? 4 and 9? 4 and 1? 4 and 2? 4 and 4? 4 and 7?

5. How many are 5 and 3? 5 and 4? 5 and 7? 5 and 8? 5 and 9? 5 and 2? 5 and 5? 5 and 6 ? 5 and 1?

6. How many are 6 and 2? 6 and 7? 6 and 9? 6 and 1? 6 and 6?

6 and 8 ?

6 and 4?

6 and 3? 6 and 5?

and 8? 8 and 1? 9. How many are 9 and 1 9 and 6? 9 and 8? 9 and 9? 10. James had 4 apples, Samuel gave him 6; how many had he in all?

gave him 5 more, and John

11. Gave 7 dollars for a barrel of flour, 5 dollars for a hundred weight of sugar, and 8 dollars for a tub of butter; what did I give for the whole?

12. Paid 5 dollars for a pair of boots, 12 dollars for a coat, and 6 dollars for a vest; what was the whole cost?

13. Gave 25 cents for an arithmetic, and 67 for a geography; what was the cost of both?

ILLUSTRATION. We may divide the cents into tens and units. Thus, 25 equals 2 tens and 5 units; 67 equals 6 tens and 7 units; 2 tens and 6 tens are 8 tens; and 5 units and 7 units are 12 units, or 1 ten and 2 units; 1 ten and 2 units added to 8 tens make 9 tens and 2 units, or 92. Therefore the arithmetic and geography cost 92 cents.

14. On the fourth of July 20 cents were given to Emily, 15 cents to Betsey, 10 cents to Benjamin, and none to Lydia; what did they all receive?

15. Bought four loads of hay; the first cost 15 dollars, the second 12 dollars, the third 20 dollars, and the fourth 17 dollars; what was the price of the whole?

16. Gave 55 dollars for a horse, 40 dollars for a wagon, and 17 dollars for a harness; what did they all cost?

17. Sold 3 loads of wood for 17 dollars, 6 tons of timber for 19 dollars, and a pair of oxen for 60 dollars; what sum did I receive?

ART. 18. From the solution of the preceding questions, the learner will perceive, that

ADDITION is the process of finding the sum of two or more numbers. The result obtained, is called their amount.

Addition is commonly represented by this character, +, which signifies plus, or added to. The expression 7+5 is_read, 7 plus 5, or 7 added to 5.

This character,=, is called the sign of equality, and signifies equal to. The expression 7+5=12 is read, 7 plus 5, or 7 added to 5, is equal to 12.

EXERCISES FOR THE SLATE.

ART. 19. The method of operation when the numbers are large, and the sum of each column is less than 10.

Ex. 1. A man bought a watch for 42 dollars, a coat for 16 dollars, and a set of maps for 21 dollars; what did he pay for the whole? Ans. 79 dollars.

OPERATION.
Dollars.

42

16

21

Having arranged the numbers so that all the units of the same order shall stand in the same column, we first add the column of units; thus, 1 and 6 are 7, and 2 are 9 (units), and write down the amount under the column of units. We then add the column of tens; thus, 2 and 1 are 3, and 4 are 7 (tens), which we write under the column of tens, and thus find the amount of the whole to be 79 dollars.

Amount 79

ART. 20. First Method of Proof.- Begin at the top and add the columns downward in the same manner as they were before added upward, and if the two sums agree the work is presumed to be right.

The reason of this proof is, that, by adding downward, the order of the figures is inverted; and, therefore, any error made in the first addition would probably be detected in the second. NOTE. This method of proof is generally used in business.

QUESTIONS. Art. 18. What is addition? What is the sign of addition, and what does it signify? What is the sign of equality, and what does it signify? Art. 19. How are numbers arranged for addition? Which column must first be added? Why? Where do you place its sum? Where must the sum of each column be placed? What is the whole sum called? -Art. 20. How is addition proved? What is the reason for this method of proof? Is this method in common use?