Six times 8 are 48-8 and carry 4-6 times 7 are 42 and 4 are 46—6 and carry 4-6 times 6 are 36 and 4 are 40—0 and carry 4—6 times 5 are 30 and 4 are 34.

Third.

Seven times 8 are 56-6 and carry 5-7 times 7 are 49 and 5 are 54-4 and carry 5-7 times 6 are 42 and 5 are 47-7 and carry 4-7 times 5 are 35 and 4 are 39.

Fourth,

Eight time 8 are 64-4 and carry 6-8 times 7 are 56 and 6 are 62—2 and carry 6-8 times 6 are 48 and 6 are 54-4 and carry 5-8 times 5 are 40, and 5 are 45.

Add the intermediate Product.

Total product in words, Forty-nine million seven hundred and sixty-seven thousand six hundred and seventy.

Product, 6 45,4 9 8,0 0 0||34-4 and carry 3—4 times 9 are 36 and 3 are 39.

Second.

Five times 7 are 35—5 and carry 3-5 times 8 are 40 and 3 are 43-3 and carry 4-5 times 9 are 45 and 4 are 49.

Third.

Six times 7 are 42-2 and carry 4-6 times 8 are 48 and 4 are 52-2 and carry 5-6 times 9 are 54 and 5 are 59.

Add the intermediate products.

We have now a total product of 645498-annex the three ciphers, that is, place them on the right hand of these figures and they will make the answer required, viz: 645,498,000.

Product in words, Six hundred and forty-five million four hundred and ninety-eight thousand.

KEY TO CARD No. 21.

Multiply by the two figures, add the intermediate products, then count the ciphers and annex them to the total pro

Product, 6 5,2 4, 8 0 0 0||duct.

First.

Six times 8 are 48-8 and carry 4-6 times 7 are 42 and 4 are 46-6 and carry 4-6 times 0 is 0 but 4 is 4-6 times 4 is 24.

Second.

Once 8 is 8-once 7 is 7—once 0 is 0, once 4 is 4. Add-bring down the ciphers.

Total product in words, Sixty-five million two hundred and forty-eight thousand.

KEY TO CARD No. 21.

99900

700

LESSON 9.

Multiply by the 7.

Seven times 9 are 63-3 and carry 6-7 times 9 are 63 and

6 9, 9 3 0,0 0 0 6 are 69-9 and carry 6-7

times 9 are 63 and 6 are 69.

Bring down the ciphers-They make Sixty-nine million nine hundred and thirty thousand.

How many square rods are in a piece of land 99 rods in length and 45 rods wide? Answer, 4455.

L

+ LESSON 14.

If a floor is 9 feet wide and 36 feet long, how many square feet does it contain?

+ LESSON 15.

Answer, 315.

Bought 99 bales of linen, in each bale were 50 pieces, and each piece contained 30 yards; how many yards were in the whole? Answer, 148500.

+ LESSON 16.

A farmer sold 45 oxen at 50 dollars a head, 30 cows at 25 dollars a head, and 99 sheep at 3 dollars a head; what was the amout of the whole ?

+ LESSON 17.

Answer, $3297.

Bought 25 bales of broadcloth, each bale contained 15 pieces, and each piece 30 yards; what did the whole cost at 9 dollars a yard? Answer, $101250. + LESSON 18.

If you pay a man 2 dollars a day, what will be the amount of his wages in 4 years, allowing 52 weeks to a year and 7 days to a week, but deducting at the same time 52 days in each year for Sundays?

+ LESSON 19.

Answer, $2496.

How much wine in 13 casks, each containing 115

gallons?

Answer, 1495.

+ LESSON 20.

What is the product of 6 dozen dozen, multiplied by half a dozen dozen?

Answer, 62208.

LECTURING.

What do we understand by the word NOTATION? Notation is the recording or noting any number of objects or things in Arithmetic it signifies the writing down any number of figures, as 1 2 3 4.

What is meant by NUMERATION?

The act of numbering after figures are noted or written; for instance, read the figures, 1, 2, 3, and 4, thus, One thousand two hundred and thirty-four.

What is ADDITION?

Addition is the combining of several numbers together, as, 3 more 5, more 6, more 7, equal 21. Or, 3 added to 5, added to 6, added to 7, cqual 21 for a RESULT OF SUM TOTAL.

What do we understand by the word SUBTRACTION? Subtraction is the lessening of any quantity, as the number 15 taken from 20, leaves 5 for a REMAINDER. What is the arithmetical name of the Subtraction?

upper number in

Call it MAJOR: the middle number we will call MINOR, and the lowermost number, Remainder.

NOTE. This Rule partakes of the nature of Division, as for example, subtract 4 from 24, five times, the remainder will be 4, the same as the quotient of 24 when divided by 6: that is, 24 less 4, equals 20; 20 less 4, equals 16; 16 less 4, equals 12; 12 less 4, equals 8; 8 less 4, equals 4. Or how many times 6 in 24? 4 times.

What is MULTIPLICATION?

Multiplication is the increasing of numbers with rapidity, instead of a tedious and slow way of operating by Addition, thus, 5 times 8 are 40; instead of 8 and 8 are 16, and 8 are 24, and 8 are 32, and 8 are 40.

By what name shall we call the terms in this Rule?

The number to be multipled is called MULTIPLICAND; the number we multiply by, MULTIPLIER; and the lowermost number PRODUCT. The Multiplicand and Multiplier are also called Factors; and may be termed upper and lower Factor.

NOTE.--When the lower factor consists of several figures, that is, a composite number, there will be more products than one, and they may be called intermediate products.

How shall we define Division?

Division is a concise way of working Subtraction, or of appropriating a larger number into smaller and equal parts; as, 41 dollars divided between 5 men, will give each man 8, and 1 over for a Remainder. This mode is