Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

then 7 times 2 (hundreds) are 14 (hundreds) and 3 which were reserved are 17 (hundreds). The answer is 1778 cents; and since 100 cents make a dollar, we may say 17 dollars and 78 cents.

The process of multiplication, by a single figure, may be expressed thus : Multiply each figure of the multiplicand by the multiplier, beginning at the right hand, and carry as in addition.

IV.

What will 24 oxen come to, at 47 dollars apiece ? It does not appear so easy to multiply by 24 as by a num ber consisting of only one figure ; but we may first find the price of 6 oxen, and then 4 times as much will be the price of 24 oxen.

Operation.

47
6

282 dolls. price of 6 oxen.

4

1123 dolls. price of 24 oxen.
Or thus 47

4

188 dolls. price of 4 oxen.

6

1128 dolls. price of 24 oxen. A number which is a product of two or more numbers is called a composite or compound number. The numbers, which, being multiplied together, produce the number, are called factors of that number. 4 is a composite number, its factors are 2 and 2, because 2 times 2 are 4. 6 is also a composite number, its factors are 2 and 3. The numbers 8, 9, 10, 12, 14, 15, &c. are composite numbers; some of them have only two factory, and some have several. The sign X, a cross, in which neither of the marks is either horizontal or perpendicular, is used to express multiplication. Thus 3 X 2= 6, signifies 2 times 3 are equal to 6.2 X 8 X5= 30, signifies 3 times 2 are 6, and 5 times 6 are 30.

any number consisting of 1, with any number of zeros at the right of it it is sufficient to annex the zeros to the multipli cand.

1 x 10 = 10 1 x 100 = 100
2 x 10 = 20 3 x 100 = 300
3 x 10 = 30 5 x 100 = 500

10: 270

4200 368 X 1000 = 368000

27 x 42 x

100 =

VI. When the multiplier is 20, 30, 40, 200, 300, 2000, 4000, &c. These are composite numbers, of which 10, or 100, or 1000, &c. is one of the factors. Thus 20 = 2 X 10; 30= 3 X 10; 300 = 3 X 100; &c. In the same manner 387000 = 387 X 1000.

How much will 30 kogsheads of wine come to, at 87 dollars per hogshead ?

Operation.

87
3

261 dolls. price of 3 hhds.
10

2610 dolls. price of 30 hhds.

More simply thus

37
30

2610 dolls. price of 30 hhds.

It appears that it is sufficient in this example to multiply by 3 and then annex a zero to the product. If the number of hogsheads had been 300, or 3000, two or three zeros must have been annexed. It is plain also that if there are zeros on the right of the multiplicand, they may be omitted until the multiplication has been performed, and then annexed to the product.

VII. A man bought 26 pipes of wine, at 143 dollars a pipe; how much did they come to ? 26 = 20+ 6. The operation may be performed thus :

143

6

858 dolls. price of 6 pipes

143
20

2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes

= 3718 dolls. price of 26 pipes
The operation may be performed more simply thus ;

143
26

2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes

= 3718 dolls. price of 26 pipes
Or multiplying first by 6:

143
26

858 dolls. price of 6 pipes + 2860 dolls, price of 20 pipes

= 3718 dolls. price of 26 pipes If the wages of 1 man be 438 dollars for 1 year, what will be the wages of 234 men, at the same rate ?

Operation.

438
234

87600 dolls. wages of 200 men + 13140 do. wages of 30 men + 1752 do. wages of 4 men

102492 dolls. wages of 234 men

any number consisting of 1, with any number of zeros at the right of it it is suficient to annex the zeros to the multipli cand.

1 X 10 = 10 1 x 100 = 100
2 x 10 = 20 3 x 100 = 300
3 x 10 = 30 5 X 100

500
10 270
100 =

4200
368 X 1000 = 368000

[ocr errors]

27 X 42 X

VI. When the multiplier is 20, 30, 40, 200, 300, 2000, 4000, &c. These are composite numbers, of which 10, or 100, or 1000, &c. is one of the factors. Thus 20 = 2 X 10; 30 = 3 X 10; 300 =3 X 100; &c. In the same manner 387000 = 387 X 1000.

How much will 30 hogsheads of wine come to, at 87 dollars per hogshead ?

Operation.

87
3

261 dolls. price of 3 hhds.
10

2610 dolls. price of 30 hhds.

More simply thus

37 30

2610 dolls. price of 30 hhds.

It appears that it is sufficient in this example to multiply by 3 and then annex a zero to the product. If the number of hogsheads had been 300, or 3000, two or three zeros must have been annexed. It is plain also that if there are zeros on the right of the multiplicand, they may be omitted until the multiplication has been performed, and then annexed to the product.

VII. A man bought 26 pipes of wine, at 143 dollars a pipe ; how much did they come to ? 26 = 20 + 6. The operation may be performed thus :

143

6

858 dolls. price of 6 pipes

143
20

2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes

= 3718 dolls. price of 26 pipes
The operation may be performed more simply thus ;

143
26

2860 dolls. price of 20 pipes + 858 dolls. price of 6 pipes

= 3718 dolls. price of 26 pipes
Or multiplying first by 6:

143
26

858 dolls. price of 6 pipes + 2860 dolls, price of 20 pipes

= 3718 dolls. price of 26 pipes If the wages of 1 man be 438 dollars for 1 year, what will be the wages of 234 men, at the same rate?

Operation.

438 234

87600 dolls. wages of 200 men + 13140 do. wages of 30 men + 1752 do. wages of 4 men

= 102492 dolls. wages of 234 men

« ΠροηγούμενηΣυνέχεια »