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987654321

Look for first figure 9 in the 123456789 column of single figures, and the number in the same line or hori8888888889 zontal row is the first product, and in the same manner we find the products by the other figures of the multiplicand successively, which we place and add as before taught.

7901234568

6913580247

5925925926

4938271605

3950617284

2962962963

1975308642

987654321

121932631112635269

To prove Multiplication.

Make the number which was the multiplicand, multiplier, then multiplying as usual, if the product be the same, the work is right.

Thus to prove the first Example in Case II.

Multiply 517
by 3042

1034

2068

15510,

1572714 Product the same as

there found.

QUESTIONS in MULTIPLICATION.

2. What doth Multiplication teach?

A. From two numbers given to find a third, which shall contain one of the given numbers as often as the other Contains unity.

2. What are the numbers called?

A. 1. The number to be multiplied is called the Multiplicand; the number we multiply by, the Multiplier; and the number found, the Product.

2. How is Multiplication performed when the multiplier is a single figure?

4. Of th' units o' th' multiplicand
And given figure, th' product find;
Put down the product units, and
The tens (if any) keep in mind:
The given tens next multiply:
The product of these tens increase
By the tens reserved by :

And so proceed from place to place.

2. When the multiplier is any number, or consists of several figures.

A. 1. Multiply the multiplicand by the units figure of the multiplier; then by tens, and so successively by every other figure.

2. Let the units figure of each product stand in the same place with the multiplying figure, &c.

3. Add all the products together.

2. When cyphers are intermixed with the significant figures of the multiplier?

A. Multiply the significant figures only, still observing to put the units figure of the product in the same place with the multiplying figure.

2. How must we prove the work of Multiplication? A. Make the multiplicand multiplier.

2. Repeat the Multiplication Table ?

A. Twice 2 is 4, &c.

CHAP. V.

DIVISION.

IVISION teacheth to find how often one given num

Dver is contained in another.

The number which divides is called the Divisor.

The number which is to be divided is called the Dividend.

And the number found by dividing the greater by the less is called the Quotient.

Case I.

When the divisor is a single figure, and the dividend no more than two, and the divisor measures the dividend.

Rule.

Consider what number multiplying the divisor will pro duce the dividend, and that number is the quotient.

Examples:

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Consider what number multiplying the divisor will make a product next less than the dividend, and that is the quotient figure sought.

2. Multiply the divisor by the quotient figure, and place the product under the dividend.

3. Subtract the product from the dividend, and if the remainder be less than the divisor, the quotient figure is truly taken.

[9]

2)15

[13]

5)28

Examples.

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When the divisor is a single figure and the dividend any number.

Rule.

Take the divisor in the last or highest figure of the dividend, if it be greater than the divisor, but if not, find how often the divisor is contained in the two last figures of the dividend, and having found the quotient figure, proceed exactly as in the last section, and find the remainder, as there taught.

2. To the remainder (if any) bring down the next lower figure, and let the number expressed by these two figures be esteemed a new dividend; or if there be no remainder, then esteem the next lower figures of the dividend a new dividend, which divide in like manner as in last section, and place the quotient figure to the right hand of that first found.

3. Proceed in the like manner from figure to figure, till the figures of the dividend be taken down successively one by one.

Case II.

When the divisor is any number whatever,

The

The process is exactly the same as in last case, only the difficulty of determining the quotient figure is greater, to render which easy, observe the following rules:

1. By means of the last, or two last figures of the divisor compared with as many, if greater, or, if not, one more of the dividend, discover the quotient figure as near as may be.

2. If the product of the quotient figure multiplied by the divisor be greater than the assumed member of the dividend, the quotient figure is too great, wherefore make it less.

3. If the remainder, after the product is subtracted from the divided member, be greater than the divisor, the quo tient figure is too little and must be made greater.

4. If neither of these happen, the quotient figure is truly found.

QUESTIONS and PRACTICAL EXAMPLES.

2. What is Division?

4. The finding how often one given number is contained in the other.

2. What are the given numbers called?

A. The lesser is called the divisor, (i. e. the divider,) and the greater the dividend, (i. e. the number to be divided.) 2. What is the number found called?

A. The quotient, which shews how often the divisor is contained in the dividend.

2. How is the quotient found?

A. Seek how often the divisor is contain'd

I' th' leading figures of the dividend ;

So the first quotient's figures found; which by
The giv'n divisor we must multiply;

The product take from what we did divide;
Next figure put by the remainder's side:
Repeat the process, until one by one,
The figures of the dividend are gone.

2. How shall I know when the quotient figure is truly found?

A. When the product of the said figure and the divisor is less than the divided member; and the remainder less than the divisor.

2, Suppose

2. Suppose I bring down the next figure of the divi dend to the remainder, and the number is still less than the divisor?

A. Put O for the quotient figure, and take down the next figure of the dividend.

2. How must I prove Division?

A. Multiply the quotient by the divisor (adding in the remainder, if any) and if the product be equal to the dividend, the work is right.

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It is usual in Practice to put down the quotient only, performing the rest of the operation by memory.

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