ence add the upper figure, which being set down, you must add one to the lower figure of the next column, for that which you borrowed; and thus proceed through the whole.

PROOF.

Add the remainder and the less number together; if the work be right, the amount will be equal to the greater number: Or, subtract the remainder from the greater sum, and the difference will be equal to the less.

From 3724 Minuend
Take 2583 Subtrahend

1141 Remainder

Proof 3724

EXAMPLES.

The operation of this example is very plain. The two sums being written down according to the rule, we draw a line underneath, and beginning at the right hand figure, say-3 from 4 leaves 1, which we set down-in the next column, the subtrahend (8) being greater than the minuend, we add 10 to the upper figure, making it 12, and say, 8 eight from 12, there remain 4, which is written down. We now carry 1 to the next column, for that which we just borrowed, and say, 1 to 5 is 6, and 6 from 7 leaves 1, which we put down; and in the next column, taking 2 from 3, leaves 1, which we write down, and the work is done. The method of proof will be extremely easy to the learner.

REMARK.-At every stage of the scholar's progress, it would be well for him to review his previous studies-to fix in his memory the most important rules; and endeavour to understand thoroughly the reasonableness and accuracy of the principles he is taught. The simple rules of arithmetick are easily acquired; but if the scholar hurries over them, as is too often the case, without fully understanding their meaning and application, he will find his subsequent studies as much retarded, as he would find them aided, were he to become MASTER OF HIS SUBJECT as he goes along.-The instructor should question his pupil on every rule, and explain the principles of the rules, in every case, where the scholar desires it.

IV. MULTIPLICATION.

MULTIPLICATION teaches how to increase the greater of twe numbers given, as often as there are units in the less; performs the work of many additions in the most compendious manner; brings numbers of great denominations into small, as pounds into shillings, pence, or farthings, &c.; and, by knowing the value of one thing, we find the value of many.

There are three parts in Multiplication, viz.

The sum to be multiplied is called the Multiplicand.
The sum by which you multiply is called the Multiplier.
The result of the operation is called the Product.

The Multiplicani and Multiplier are likewise called both together factors, or that by which the operation is performed.

SIMPLE MULTIPLICATION

Is the multiplying of any two numbers together, without having regard to their signification; as, 7 times 8 are 56, &c.

RULE.

1. Place the Multiplier under the Multiplicand, so that units stand under units, tens under tens, &c., and draw a line under them.

2. Beginning at the right hand, multiply each figure in the multiplicand by each in the multiplier, placing the first figure of every line directly under its respective multiplier, and to the product of the next figure carry one for every ten, as in addition. 3. Add the several products together, and their sum will be the total product required.

PROOF.-Multiply the multiplier by the multiplicand.*

It is indispensably necessary that the Multiplication Table be comm tted perfectly to memory, before the scholar proceeds to the examples under the rules.

* The better way of proving Multiplication, is by Division. It may also be proved by casting out the 9's; but as the work will sometimes prove by that method, when in fact wrong, the rule is omitted.

28. What is Multiplication?—~ 29. What are the terms used in multiplication?30. What is the multiplicand?-31. What the multiplier ? product?- 33. What are the two first sometimes called?Multiplication?. -35. What is the general rule for multiplying

32. And what is the 34. What is Simple simple numbers ?~

3. How do you prove your sum to be right ?-37. Repeat the Multiplication Table,

EXAMPLES.

1. What is the product of 90631, multiplied by 8 ?

Multiplicand,
Multiplier,

Product,

90631

725.048

Here, in the first place, we write down the multiplicand; then we write the multiplier under the unit figure of the multiplicand, and draw a line underneath. We then say, 8 times 1 are 8; as the product does not exceed nine, we write it underneath; we then say, 8 times 3 are 24, we write down the right hand figure 4, and reserve the left hand figure 2, to be added to the product of the next figure; we then say, 8 times 6 are 48 and two are 50, we write down the right hand figure 0, and reserve the left hand figure 5, to be added to the product of the next figure; we then say, 8 times 0 is 0 and 5 are 5, and write down 5; we then say, 8 times 9 are 72: this being the last figure, we write down the whole product 72, and find the answer to be 725.048.

5. What will be the product of 25.375, multiplied by 10?

6. Multiply 750.005 by 11.

7. Multiply 900.301.399 by 12.

8. Multiply 989.000 by 9.

9. Multiply 568.098 by 8. 10. Multiply 639.408 by 10. 11. Multiply 789.795 by 7.

CASE I.

When the Multiplier consists of several figures.

RULE.-Write down the multiplicand, and under it the multiplier, units under units, tens under tens, &c. Then multiply by each significant figure in the multiplier separately, beginning with units, and writing the first figure of each different product directly under the figure by which you are multiplying. Add the several products together, and you have the sum total.

38. What is your rale, when the multiplier consists of several figures?