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23. Multiply 4926 by 6. Multiply 4829 by 7. 24. Multiply 3624 by 4. Multiply 1684 by 2.

25. If it takes 5428 shingles for the roof of a house, how many shingles will it take for 5 such houses ?

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FIRST PROCESS.

37

1. Multiply 435 by 37.

EXPLANATION.—The numbers are

written as before. Since in multiply. 425

ing we multiply by the parts of a

number, to multiply by 37 we multi7 x 425 = 29 7 5

ply by 30 and by 7, and add the re

sults. 30 X 425 =12750

7 times 425 are 2975, the first par37 X 425=15725 tial product; 30 or 3 tens times 425

are 1275 tens or 12750, the second partial product. The sum of these partial products will be the entire product.

Hence the entire product is 15725.

SECOND PROCESS.

EXPLANATION.-In this process the

cipher at the right of the partial prod425

uct is omitted and the significant figures 37

placed in their proper places. Thus, in 7 X 425= 29 75

multiplying by 3 tens, the product is

1275 tens or 12 thousands 7 hundreds 3 X 425=1275

and 5 tens, which are written in their 157 25 proper places in the partial product. In multiplying by tens the lowest denomination of the product is tens, in multiplying by hundreds it is hundrels, by thousands it is thousands. Hence,

The first figure of each product should be placed under the figure by which we multiply.

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1. How many barrels of flour at 8 dollars a barrel, can be bought for 72 dollars ?

2. If there are 3 feet in a yard, how many yards are there in 27 feet?

3. At 4 dollars a cord, how many cords of wood can be bought for 40 dollars ?

4. If a man can walk 4 miles per hour, how long will it take him to walk 36 miles?

5. If 5 paces are a rod of distance, what is the length in rods of a piece of land which is 30 paces long?

6. If paper is put in packages containing 6 sheets each, how many packages can be made out of 48 sheets ?

7. If 5 bushels of wheat make a barrel of flour, how many barrels of flour can be made from 40 bushels of wheat ?

8. At 6 dollars a ton, how many tons of hay can be bought for 54 dollars ?

9. If a man can build 7 rods of fence in one day, in how many days can he build 35 rods?

10. If a teacher earns 9 dollars a week, in how many weeks can she earn 90 dollars ?

DEFINITIONS.

The process of finding how many times one number is contained in another is called Division.

The number to be divided is called the Dividend.

The number by which the dividend is to be divided is called the Divisor.

The result in division is called the Quotient,

The part of the dividend remaining when the division is not exact is called the Remainder.

The Sign of Division is -, read divided by.
Thus, 24 :- 6 is read, 24 divided by 6.

FIRST PROCESS.

1. How many times is 3 contained in 369 ?

EXPLANATION. — For convenience Divisor. Dividend. Quotient. the divisor is written at the left of the

3) 3 6 9 (100 dividend, and the quotient at the right.
300 20 Beginning at the left we divide.
3

3 is contained in 369 1 hundred 69

times and a remainder. The 100 is 60 123

placed in the quotient, and the divisor 9

is multiplied by it. The product 300 9

is written under the dividend. Sub

tracting there is a remainder of 69. 3 is contained in 69, 20 times and a remainder. The 20 is placed in the quotient and the divisor multiplied by it. The product 60 is written under the partial dividend. Subtracting the remainder is 9.

3 is contained in 9, 3 times and no remainder. The 3 is placed in the quotient, and the divisor multiplied by it. The product 9 is written un the partial dividend. Subtracting, there is no remainder.

The true quotient is therefore the sum of the partial quotients, which is 123, and 3 is contained in 369, 123 times.

SECOND PROCESS.

hund.

W tens.

units.

EXPLANATION.—The second process is the same as the first, except that the ciphers

are vmitted from the right of the quotient 3)36 9(123

figures and partial products, the value of 3

figures being indicated by their position. 6

Thus, the figures of the quotient are 1 hun6

dred, 2 tens, and 3 units, which are written

in succession so that each figure represents 9

its proper value. 9

The products 3 hundreds, 6 tens and 9

units are placed under hundreds, tens, and units in the partial dividends.

CO CO

SLATE EXERCISES. Copy and divide the following:

(2.) (3.) (4.) 4) 488 ( 5) 550( 3) 699 (

(5.) 2) 264

LESSON LXXVI.

1. How many times is 6 contained in 1398 ?

PROCESS.

EXPLANATION.–For convenience the di.

visor is written at the left of the dividend 6)1398(233 12

and the quotient at the right. Beginning

at the left of the dividend we divide. 19

6 is not contained in 1 thousand any 18

thousand times, therefore the quotient can 18 not be higher than hundreds.

Hence we 18

must find how many times 6 is contained in all the hundreds of the dividend.

1 thousand is equal to 10 hundreds. 10 hundreds plus 3 hundreds equal 13 hundreds. 6 is contained in

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