dolls. How much did he borrow, and how much does he still owe? Answer. Borrowed 425. Owes 150.

7. On a certain farm there are 750 apple-trees, 425 peartrees, 1000 peach trees, and 389 plum-trees. What is the amount of the whole, and how many more apple-trees than pear-trees, and how many more peach than plum?

8. A man left to his wife 2500 dollars, to his four sons 900 dollars each, to his three daughters 450 each. What was the amount of property left, and how much more was left to the mother than to the daughters, and to the sons more than to the mother?

5. The reforD. 1517; the

9. There were five important events in the course of 215 years, viz.-1. The invention of the mariner's compass. 2. The invention of gun-powder. 3. The art of printing. 4. The discovery of America. mation. The last was accomplished, A. third, 77 years before; the second, 42 years after the first, and the fourth 148 years after the second. The question is, In what year did each happen?

Answer. Mariner's compass in 1302, gun-powder in 1344, Printing 1440, Discovery of America, 1492.

MULTIPLICATION.

1. If Mary give 4 cents for one picture-book, how much must she give for 2 books? how much for 4? how much for 5?

2. If one dozen of eggs cost 10 cents, how many cents will two dozen cost? how many will 4? 5? 6?

3. If one share in a library cost 5 dollars, how much will three shares cost? how much 4? how much 5? how much 6?

4. If a picture frame cost 12 dollars, what will 4 cost? what will 6? what will 7? what will 8? what will 9?

5. Four men bought a piece of land, each paying 12 dollars. What did they all pay?

6. If a horse can trot 11 miles in one hour, how many miles can he travel in 8 hours? how many in 10? in 12? 7. If a bushel of wheat cost 2 dollars, how many dollars will 8 bushels cost? how many will 9? how many will 10? how many will 11? how many will 12?

8. If a man receive 4 shillings for a day's work, how much will he receive for a week's work?

9. A pound of sugar is worth 3 cents. —7—8—9—10—11-12 pounds worth?

What are 6

10. John bought a writing-book for 6 cents. What will 2 cost? what will 4? what will 6? what will 8 ?

II. If a bushel of potatoes cost 32 cents, what will 3 bushels cost? what will 4? what will 6?

12. If a steam-boat sail 8 miles in one hour, how many will she sail in 12 hours?

The scholar should commit to memory the following TABLE before proceeding any further.

MULTIPLICATION AND DIVISION TABLE.

1 make 8 1 make 9 1 make 10 1 make

11 1 make 12

13. If a man pay 85 dollars for a carriage, what must he pay for 5 carriages?

The answer may be obtained by setting down 85, five times, and adding them up, thus:

85

85

85

It will be seen by examining this operation, that the product of five times five units is two tens and five units, and five times eight tens is 40 tens. The answer, then, is 40 tens, 2 tens and 5 units, or 425. This method, in long sums, would be tedious, and can be resolved much easier by multipli- 425 cation, thus:

85
5

425

Instead of setting down 85, five times, we write 5, the muitiplier, under the unit figure of the number to be multiplied; then say, 5 times 5 are 25, setting down 5, the excess of tens, and reserving, in the mind, 2, the number of tens; we say 5 times 8 are 40, adding the two tens which we reserved from the unit column, we set down 42. The answer, then, is 42 tens and 5 units, or 425.

From the above we derive the following definition :— Multiplication is a concise method of performing many additions. Two numbers are required to perform the operation. The number to be multiplied is called the Multiplicand. The number by which we multiply is called the Multiplier. Taken together they are called Factors. The answer obtained is called the Product.

14. If a share in a bridge is worth 142 dollars, how many dollars are 6 shares worth?

Operation.

142

6

852 Answer.

QUESTIONS. 1. What is Multiplication? 2. How many numbers are required to perform the operation? 3. What is the number to be multiplied called? 4. What is the number by which you multiply, called? 5. Taken together, what are they called? 6. What is the answer called? 7. How many figures are there in the multiplier of the 14th question?

15. If a man receive 164 dollars for a year's labour, what will 32 men receive for the same time?

164

32

328

492

5248

12 being the largest number by which we can multiply collectively, it will be necessary in this example to adopt a different mode of operation. The multiplier consists of 3 tens and 2 units, and multiplying by the 2 units, we obtain for a product, 328. We then multiply by the three tens, setting the product, 2, in the place of tens, because it is the product of tens. We next multiply the 6 tens of the multiplicand by the three tens of the multiplier, carrying one for every ten, as in Addition. The product of ten multiplied by ten is hundreds; we, therefore, set it down in the place of hundreds. Lastly: we multiply the hundreds in the multiplicand by the tens in the multiplier, and set the product in the place of thousands. The product of hundreds multiplied by ten is thousands. Adding together the several products we have 5248, the answer.

From the foregoing examples we derive the following

RULE.

I. Place the multiplier directly under the multiplicand, units under units, tens under tens, &c., then draw a line underneath.

II. When the multiplier is 12, or less than 12, begin at the right hand of the multiplicand, and multiply each figure contained in it by the multiplier, setting down the numbers, and carrying as in Addition.

III. When the multiplier is greater than 12, write down the figures as before directed, and multiply the multiplicand by each figure in the multiplier, commencing with the unit figure; observing to place each figure in the product directly under the figure by which you multiply. In this way proceed, and the sum of the products will be the answer.

QUESTIONS. 8. By which do we multiply first? 9. What is the product of units multiplied by units? 10. Of tens multiplied by tens? 11. Of hundreds by hundreds? 12. How are the numbers placed in multiplication? 13. How do you proceed when the multiplier is 12 or less than 12? 14. When the multiplier is greater than 12 ?

PRACTICAL EXAMPLES.

9. What will 432 barrels of flour cost, at 14 dollars a barrel? Answer, 6048 dollars. 10. How many rods in 84 miles, there being 320 rods in a mile? Answer, 26880 rods. 11. What will be the cost of 6328 thousands of boards, at 18 dollars per thousand? Ans. 113904 dollars.

12. What will 64 cows cost, at 16 dollars apiece? Answer, 1024 dollars. The multiplier, 16, in the last example, is a number which can be formed by the multiplication of two numbers —thus: 4×4=16: or 8×2=16. Any number thus produced is called a composite number. The numbers thus multiplied are called component parts. Sixteen, then, is a composite number, and 4 & 4, or 8 & 2 are the component parts of 16. Thus, taking the above question, 64×4 = 256, the price of 64 cows at 4 dollars each, and this product multiplied by 4 gives 1024, the price at 16 dollars each, because 4 times are 16. The same result will be produced if we multiply 64 by 8 and 2.

RULE.

When the multiplier is a composite number, multiply first by one of the component parts, and that product by the other, and so on, if there be more than two; the last product will be the answer.

QUESTIONS. 15. What is a composite number? 16. What are the numbers called which form a composite number? 17. What is the rule for multiplying by a composite number?"