RULE.

I. Place the multiplier under the multiplicand, so that units may stand under units, tens under tens, hundreds under hundreds, &c.

II. Multiply successively by each figure of the multiplier, as in Case I., observing to place the right-hand figure of each partial product directly under the figure multiplied by.

III. Then add together these partial products, and the sum will be the total product sought.

When the multiplier consists of more than one figure, how do you write it? How do you then multiply? How do you add up?

9. Multiply 3471032 by 70056. Ans. 243166617792.

10. Multiply 1240578 by 302014.

Ans. 374671924092.

11. Multiply 235678 by 753465.

Ans. 177575124270.

12. Multiply 98610275 by 35789.

Ans. 3529163131975.

CASE III.

20. When the multiplier, or multiplicand, or both, have one or more ciphers at the right.

We know from what has been said, (ART. 4,) that multiplying by 10 is the same as annexing a cipher to the right of the figure or sum to be multiplied; multiplying by 100 is the same as annexing two ciphers to the right of the figure or sum to be multiplied, &c.

Hence we deduce this

RULE.

Multiply by the significant figures,(as in Case II.) and to the product annex as many ciphers as there are in both mul tiplier and multiplicand.

When there are ciphers at the right of the multiplier, or multiplicand, or both, how do you proceed?

CASE IV.

21. When the multiplier is a composite number.

A composite number is one which may be produced by multiplying two or more numbers together. Thus: 35 is a composite number, which may be produced by multiplying 5 and 7 together.

The 5 and 7 are called the factors or component parts of 35.

The factors of 12, are 3 and 4, or 2 and 6.

Suppose we wish to multiply 48 by 35.

If we first multiply 48 by 5, we find 240 for the product; if now we multiply this product by 7, we obtain 1680, which is evidently the same as 35 times 48. Hence we infer this

RULE.

Multiply the sum given by one of the factors, and this product by another factor, and so on, until all the factors are used. The last product will be the one sought.

EXAMPLES.

1. Multiply 365 by 28.

The factors of 28 are 4 and 7. Hence we have this

OPERATION.

365

4 one of the component parts.

1460

7 the other component part.

10220 Ans.

2. Multiply 374 by 24 = 4 x 6 3 x8 = 2 × 12 =

From the above examples, we see that it makes no difference how we resolve the multiplier into factors, provided we multiply in succession by all the factors.

you

What is a composite number? What are the component parts? How do proceed when the multiplier is a composite number? Does it make any difference which component part we first multiply by }

3. Multiply 345678 by 36 = 6 × 6=4×9 = 3 × 12 = 3 x 3 x 4. Ans. 12444408.

duce of each tree is 7 barrels of fruit, worth 3 dollars per barrel. What was the income of the orchard?

1

Ans. 2205 dollars.

DIVISION OF SIMPLE NUMBERS.

22. DIVISION teaches the method of finding how many times one number is contained in another.

The number to be divided is called the dividend.

The number by which we divide is called the divisor. The number of times which the dividend contains the

divisor is called the quotient.

Besides these three parts there is sometimes a remainder, which is of the same name as the dividend, since it is a part of it.

The sign usually employed to indicate division is. Thus, 123, denotes that 12 is to be divided by 3.

By using this sign we may form the following