3. When there are cyphers between the fignificant figures of the Multiplier, omit the cyphers, and multiply by the fignificant figures only, placing the first figure of each product directly under the figure by which you muitiply, and adding the products together, the fum of them will be the product of the given numbers.

4. When the Multiplier is 9, 99, or any number of 9's, annex as many cyphers to the Multiplicand, and from the number thus produced, fubtract the multiplicand, the remainder will be the product.

Supplement to Multiplication.

QUESTIONS.

1. What is Simple Multiplication?

2. How many numbers are required to perform that operation? 3. Collectively, or together, what are the given numbers called? 4. Separately, what are they called?

5. What is the result, or number fought, called?

6. In what order must the given numbers be placed for multiplication?

7. How do you proceed when the multiplier is less than 12?

8. When the multiplier exceeds 12, what is the method of procedure? 9. What is a compofite number?

10. What is to be understood by the component parts of any number? 11. How do you proceed when the multiplier is a compofite number? 12. When there are cyphers on the right hand of the multiplier, multiplicand, either or both, what is to be done?

13. When there are cyphers between the fignificant figures of the multiplier how are they to be treated ?

14. When the multiplier confifts of 9's, how may the operation be con

tracted?

15. How is Multiplication proved?

16. By what method do' you proceed in cafting out the 9's from any number?

17. How is Multiplication proved by cafting out the 9's?

18. Of what use is Multiplication?

EXERCISES.

1. What fum of money must be divided between 27 men fo that each may receive 115 dollars? Ans. 3105.

NOTE. The fcholar's business in all questions for Arithmetical operations, is wholly with the numbers given; these are never lefs than two; they may be more ; and these numbers, in one way or another, are always to be made ufe of to find the answer. To thefe therefore, he must direct his attention, and carefully confider what is proposed by the question, to be known.

§ 4. Simple Division.

SIMPLE DIVISION teaches, having two numbers given of the fame denomination, to find how many times one of the given numbers contains the other. Thus, it may be required to know how many times 21 contain 7, the answer is 3 times. The larger number (21) or number to be divided, is called the Dividend; the lefs number, (7) or number to divide by, is called the Divifor; and the answer obtained, (3) the Quotient.

After the operation, fhould there be any thing left of the dividend, it is called the Remainder. This part, however, is uncertain; fometimes there is no remainder. When it does happen, it will always be less than the divifor, if the work be right, and the fame name with the dividend.

RULE.

1. “Affume as many figures on the left hand of the dividend, as contain "the divifor once or oftener; find how many times they contain it, and place the answer as the highest figure of the quotient.

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2. "Multiply the divifor by the figure you have found, and place the "product under that part of the dividend from which it was obtained.

3. "Subtract the product from the figures above it.

4. "Bring down the next figure of the dividend to the remainder, and di"vide the number it makes up as before."

When you have brought down a figure to the remainder, if the number it makes up be ftill lefs than the divifor, a cypher must be placed in the quotient, and another figure brought down.

1. Divide 127 by 5. Divifor. Dividend. Quotient. 5) 127 (25

10

27
25

2 Remainder.

EXAMPLES.

The parts in Division are to stand thus, the dividend in the middle, the divifor on the left hand, the quotient on the right, with a half parenthesis feparating them from the dividend.

Proceed in this operation thus.-It being evident that the divifor (5) cannot be contained in the first figure (1) of the dividend, therefore, assume the two first figures (12) and inquire how often 5 is contained in 12, finding it to be 2 times, place 2 in the quotient, and multiply the divifor by it, faying 2 times 5 is 10, and place the fum (10) directly under 12 in the dividend. Subtract 10 from 12, and to the remainder (2) bring down the next figure (7) at the right hand, making with the remainder (2) 27. Again inquire how many times 5 in 27; 5 times; place 5 in the quotient, multiply the divifor, (5) by this last quotient figure (5) faying, 5 times 5 is 25, place the fum (25) under 27, fubtract, and the work is done. Hence it appears that 127 contains 5, 25 times, with a remainder of 2, which was left after the laft fubtraction.

This Rule, perhaps, at first will appear intricate to the young ftudent, although it is attended with no difficulty. His liability to errors will chiefly arife from the diverfity of proceedings. To affift his recollection let him notice, that 1. Find how many times, &c. 2. Multiply.

The steps of Divifion are four

3. Subtract.
4. Bring down.

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