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MULTIPLICATION. Of all the rules in Arithmetic, Multiplication is the most useful. By two given numbers, it teaches its to find out a third, which shall contain, or increase, the greater as many times as there are units in the less.

By this rule, many sums, in addition, may be wrought, in the most compendious manner.

By this rule, greater denominations are brought into smaller ; as pounds into shillings; shillings into pence; and pence into farthings.

Knowing the length and brearlth of a plain surface, we may learn, by this rule, its superficial centents, or square measure.

And by knowing the value of one thing, or the wages of one person, we are taught.. by this rule, the value of many such things, or the wages of many such persons.

The number to be inultiplied, is called the multiplicand ; that by which the number is multiplied is called the multiplier ; which is, commonly, the less number : The product is ibe result of the work, or the answer. The multiplicand and multiplier, taken together, are called the factors.

SIMPLE MULTIPLICATION, Means the multiplying of any two numbers together which are of one denomination.

Before the learner proceeds in this useful rule, he ought to kommit perfectly to his memory, the following table.

MULTIPLICATION TABLE. 2 times 2 is, 4 4 times 7 is 28 7.times 8 is 56 S 6 4 8 32 7

9 63 8 9 36 7

10 70
. 10
10 40 7

11
11
44 7

12 84
7
4
12 48 3

8 764 2 8 16 5 5 25 8

72 18 6 30

13 80 10 20 5 7 35

li 3

40

12 96 12 15 9 45

9 81 15 5 10 50

10 90 18 5 11 55 9

11 99 7 21 12 60 9

12 108 24 6 36 10

Х 10 100 9 6 7 42 10

110 10 30

8 48
10

12

120 9

11 X 11 121 -12 S6 6

10 Oy
Il

12 152 16

11 60 20

12 172 У

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TO PROVE multiplication, division is the most sure and expeditiqus mode. Or you may invert your factors, and if the product be like the former, the work is right. As the pupil is supposed not to have learned division, he may prove multiplication, by the excess of nines.

RULE. Reject all the nines out of the multiplicand, multiplier, and product, and place the excess of each directly opposite their respective terms. You must then multiply the excess of nines in the multiplicand, by the excess of nines in the multiplier ; reject all the nines from this last product, and if the excess be equal to the excess in the first product, the work is right.

CASE 1.
When the multiplier does not exceed 12.

RULE. Having placed units under units, and tens under tens, proceed, in the work, as the table directs, being careful to carry one for every ten, to the place of tens, or to the next superior row, as in simple addition.

EXAMPLES. 1. 2. 3.

5.
Multiplicand 4 36 87 4236 4623
Multiplier 2

5
6

7

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CASE 2. When the multiplier is more than 12.

RULE. Multiply separately each figure, in the multiplicand, by each figure in the multiplier, beginning with the place of units, and placing the first figure of each product directly under its multiplier ; then add the several products together, in the same ore . der, as they stand, and their sum will lps the total product.

EXAMPLES
Multiplicand 42367

42367
Multiplier 13

24

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CASE 3. When either the multiplicand, or multiplier, or both, have cyphers at the right hand.

RULE. Set the first figure of the multiplier under the first figure of the multiplicand. And then, not regarding the cyphers, proceed as in Case 1. or 2. as the operation may require. Lastly, to the product annex all the cypliers in the multiplier and mulii. plicand.

EXAMPLES
46700 43000 7800000

567000000
300
9000
700000

97000000

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74630000000

236784200000 742365700000

3623000000000
7436000000000

CASE 4.
To multiply by 10, 100, 1000, 10000, &c.

RULE. * Add as many cyphers to your multiplicand, as there are in the multiplier; and your work will be done.

EXAMPLES. 46 7423

96234 842367 7423678992 10 100 1000 10000

10000000

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CASE 5.
When cyphers are intermixed with the multiplier.

RULE. Omit to multiply by the cyphers, and place the first figure of each product directly under the figure, by which you multiply. Then add the products together, and their sum will be the total product.

EXAMPLES.
423
24393
742267

89236782
306
402
4023

403064

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We shall now teach how to apply this rule, in the real busi ness of life.

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What are the superficial contents, in feet, of a garden, 80 feet in length, and 70 in breadth ?

80 length.
70 breadth.

5600 Answer.

2. If the wages of one man, for a year, be 112 dollars, What are the wages of 24 men ?

112 dollars,
24 men.

448

224

2688 dollars, the answer.

3. If one yard of broadcloth cost 5 dollars, What is the cost of 63 yards, at the same rate ?

63 yards.
5 dollars.

315 dollars, the answer.

4. If one dozen of eggs cost 10 cents, what is the cost of 13 dozen ? Answer, 130 cents, or 1 dollar and 30 cents.

5. If one pound of flax cost 17 cents, What is the cost of 245 pounds ? Answer, 4165 cents, or 41 dollars and 65 cents.

6. If one gallon of rum cost 133 cents, What is the cost of 6 gallons ? Answer, 7 dollars and 98 cents,

7. If I give 6 cents a mile for the hire of a horse, What will a journey of 146 miles cost me? Answer, 876 cents, or 8 dol. lars and 76 cents.

8. If I give 14 cents a mile for the hire of a horse and chaise, What will a journey of 237 miles cost me? Answer, 3318 cents, or 33 dollars and 18 cents.

9. If one pound of butter cost 20 cents, What is the cost of a firkin of butter containing 86 pounds! Answer, 1720 cents, or 17 dollars and 20 cents.

10. If one pound of live geese feathers cost 75 cents, What is the cost of feathers for a bed, containing 44 pounds ? Answer, 3300 cents, or 33 dollars.

11. If one piece of nankeen cost 116 cents, What is the cost of 4 dozen pieces ? Answer, 5568 cents, or 55 dollars and 68

cents,

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