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?

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 multiplier 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 x 8 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.

What is a composite number? What are the component parts? How do you 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 x6=4×9= 3 × 12 = 3 x 3 x 4.

Ans. 12444408..

4. Multiply 1002456 by 728×9 = 2 × 3 × 3 × 4 = 2 × 2 × 2 × 3 × 3.

Ans. 72176832.

= 3 × 4 × 7=2 Ans. 633368568.

5. Multiply 7540102 by 847 × 12:

× 2 × 3 × 7.

EXERCISES IN MULTIPLICATION.

1. Suppose I buy 15 loads of bricks, each load containing 1250 bricks, how many bricks have I ?

Ans. 18750 bricks.

2. In an orchard there are 107 apple-trees, each produ How many bushels does the

cing 19 bushels of apples. whole orchard yield?

Ans. 2033 bushels.

3. If a person travel 17 days at the rate of 37 miles each day, how many miles will he travel in all?

Ans. 629 miles.

4. If a person buy 175 barrels of salt, each weighing 304 pounds, how many pounds in all will he have?

Ans. 53200 pounds.

5. Suppose I purchase the following bill of merchandise: 3 Firkins of butter, each 15 dollars.

7 Hogsheads of molasses, each 23 dollars. 12 Bags of coffee, each 11 dollars.

5 Boxes of raisins, each 2 dollars.

3 Boxes of lemons, each 5 dollars.

How many dollars must I give for the whole?

Ans. 363 dollars. 6. How many dollars will the following bill of goods amount to?

52 Yards of black broadcloth, at 4 dollars per yard. 40 Yards of Brussels carpeting, at 2 dollars per yard. 2 Sofas, each 56 dollars.