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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,) tnat 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?

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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 multiply ing 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.

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2. Multiply 374 by 24 = 4 × 6 = 3 × 8 = 2 × 12 =

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From the above examples, we see that it makes no dif ference 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 × 6 = 4 × 9 = 3 × 12 = 3 × 3 × 4.

Ans. 12444408.

4. Multiply 1002456 by 72 = 8 × 9 = 2 × 3 × 3 × 4 = 2 × 2 × 2 × 3 × 3. Ans. 72176832. 5. Multiply 7540102 by 84 = 7 x 12 = 3 × 4 × 7=2 x 2 x 3 x 7. Ans. 633368568.

EXERCISES IN MULTIPLICATION.

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

Ans. 18750 bricks.

2. In an orchard there are 107 apple-trees, each produ cing 19 bushels of apples. How many bushels does the 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.

9. Mahogany chairs, each 5 dollars.
5 French bedsteads, each 7 dollars.

Ans. 480 dollars.

7. If the railroad extending between Albany and Buffalo, a distance of 326 miles, cost 25649 dollars per mile, what was the entire cost? Ans. 8361574 dollars. 8. How many bushels of potatoes may be produced from 13 acres of land, if each acre produces 212 bushels? Ans. 2756 bushels.

9. How much must be paid for constructing 18 miles of plank-road, at 4211 dollars per mile? Ans. 75798 dollars. 10. How much will 543 cords of wood cost, at 5 dollars per cord? Ans. 2715 dollars.

11. In one year there are 8766 hours, how many hours in 1848 years? Ans. 16199568 hours.

12. In one cubic foot there are 1728 cubic inches, how many cubic inches in 17 cords of wood, each cord containing 128 cubic feet? Ans. 3760128 cubic inches. L. 13. What will 13 square miles of land cost, at 17 dollars per acre, there being 640 acres in one mile?

Ans. 141440 dollars. 14. How many miles will a steam locomotive pass in 7 days of 24 hours each, if it move at the rate of 45 miles each hour? Ans. 7560 miles. 15. If the earth move in its orbit 68000 miles per hour, how far will it move in 365 days of 24 hours each?

Ans. 595680000 miles.

16. If one mile of railroad require 116 tons of iron, worth 53 dollars per ton, what will be the cost of sufficient iron to construct a road of 78 miles in length?

Ans. 479544 dollars. 17. In an orchard of 105 apple trees the average pro

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