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27. A merchant sent out his clerk to collect money; he collected 50 dollars from one person, from a second 25, from a third 125, and from a fourth 216, how many dollars did he collect in all? Ans. 416.

28. A man set out on a journey and travelled the first day 37 miles, the second day 33 miles, the third day 40 miles, the fourth day 35 miles, how many miles was he at the end of the fourth day from the place from which he started?

Ans. 145. 29. A. has a flock of sheep containing thirty-four, B. has a flock containing forty-seven, and C. has a flock containing fifty-four, how many sheep are in all three of the flocks?

Ans. 135. 30. A butcher bought of one man, 25 head of cattle, of another 15, of another 40, and of another 9, how many did he buy in all? Ans. 89. 31. A farmer has four fields, the first contains 8 acres, the second 15 acres, the third 19 acres, and the fourth 12 acres, how many acres are there in all the four? Ans. 54.

32. A flour merchant bought from one man 400 barrels of flour, for which he gave 2000 dollars, from another man 550 barrels, for which he gave 2750 dollars, how many barrels of four did he buy, and how many dollars did he give for the whole? Ans. 950 barrels. 4750 dollars.

MULTIPLICATION

Multiplication is a short method of performing Addition when the same quantity is required to be added a given number of times.

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

Case 1.

When the Multiplier does not exceed 12.

Rule.

1. Set down the multiplicand or number to be multiplied, and under the units place of the multiplicand the multiplier or number by which you multiply.

2. Multiply each figure of the multiplicand in succession by the multiplier, set down the amount, and carry in the same manner as in addition.

Proof.-Multiply the multiplier by the multiplicand.

Note.-Multiplication and addition may likewise be proved by casting out the nines, but as the work will sometimes prove by that method when in reality wrong, the rule is omitted.

Before proceeding further, it is indispensable that the fearner should commit the following table to memory.

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Note. The multiplication table has not been usually extended further than twelve but may be extended to any number at pleasure, and if committed to memory to 50 or 100 will well repay the trouble of learning it.

Questions.

What is Multiplication?

How many parts are there in Multiplication? Name them. By what name are the multiplicand and multiplier together called?

Repeat the rule for performing Multiplication, when the multiplier does not exceed 12.

How do you prove multiplication?
Repeat the multiplication table.

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11) 456978426976 (12) 8079698769 (13) 97698429769

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When the multiplier exceeds 12, and consists of two or more figures.

Rule.

1. Set down the multiplicand and under it the multiplier, in such a manner that units may stand under units, tens under tens, hundreds under hundreds, and so on.

2. Then proceed to multiply all the figures of the multiplicand by the units figure of the multiplier, setting down the product as before.

3. After having multiplied by the units figure of the multiplier, then take the tens, hundreds, &c. proceeding in the same way with every figure, observing when you multiply by the tens figure of the multiplier to set down the first figure of the product under the tens figure of the multiplier, and when by the hundreds the first figure must be set under the hundreds of the multiplier, &c.

4. Add together the several products exactly in the places in which they stand, and you will have the last or final product.

Questions.

When the multiplier exceeds 12, and consists of two or

3

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MULTIPLICATION.

more figures, when you have set down the multiplicand how do you set down the multiplier?

How do you then proceed?

After you have multiplied by all the figures of the multiplier and set down the product in their proper places, what is

to be done to obtain the last or final product?

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When there are ciphers at the right of either the multiplicand or multiplier.

Rule.

1. Multiply as in the preceding case, only omitting the ciphers,

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