Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

3. Subtract 267 from 345 and add 150 to the remainder. Facit 228. 4. A person had in his desk 1000 dollars. He took out 120 dollars to pay a debt. He afterwards put in 75 dollars. How much was there then in the desk?

Ans. 955 dollars.

SIMPLE MULTIPLICATION.

Multiplication teaches to find what a number amounts to when repeated a given number of times.

The number to be multiplied is called the multiplicand. The number to multiply by is called the multiplier. The number produced by multiplying is called the product.

Note. The multiplier and multiplicand are also called factors.

The scholar should commit the following table to memory before he proceeds further.

[blocks in formation]

2 4 6 8 10 12 14 16 18 20 22 24

3

34

6 91215182124 27 30 33 36
4 81216|20|24|28|32 36 40 44 48
5 10 15 20 25 30 35 40
61218243036 42 48

45 50 55 60

54 60 66 72

71421 2835424956 63 70 77 84 81624 324048 5664 72 80 88 96 91827 3645546372 81 90 99108 10 20 30 40 50 60 70 80 90 100 110 120 1122334455667788 99110121132 12 24 36 48 6072|84|96|108/120 132144

When the multiplier does not exceed 12, work by

RULE I.

Set the multiplier under the units place of the multiplicand. Then, beginning with the units, multiply each figure of the multiplicand, in succession, disposing of their several products as the amounts of the columns

are disposed of in addition. Thus: if the product of the units figure do not exceed 9, set down that product: but if it exceed 9, set down its right hand figure, and add its left hand figure or figures to the product of the tens, &c.

PROOF.

Multiply by double the multiplier, and the product will be double the former product.

[blocks in formation]

Multiply by each figure of the multiplier separately, first by the one at the right hand, then by the next, and so on; placing their respective products one under ano

ther, with the right hand figure of each product directly under that figure of the multiplier by which it is produced. Add these products together and their amount will be the product required.

Note. When cyphers occur at the right hand of either or both of the factors, omit them in the operation, and annex them to the product.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

Note. When the multiplier is the exact product of any two factors in the multiplication table, the operation may be performed thus: multiply by one of the factors, and then multiply the number produced by the other factor.

[blocks in formation]
[blocks in formation]

1. Richard has 125 nuts, and George has 6 times that number. How many has George? Ans. 750.

2. There are 20 boxes of raisins with 14 pounds in each box. How many pounds are there in all? Ans. 280. 3. The price of one orange is 9 cents: how many cents will 5 oranges come to, at the same price?

Ans. 45. 4. There are 12 pence in one shilling. How many pence are there in 40 shillings? Ans. 480.

ADDITION AND MULTIPLICATION.

1. Multiply 25 by 10, and 36 by 14, and 124 by 45. Add the several products and tell their amount.

Ans. 6334.

2. There are 10 bags of coffee weighing each 120 pounds; and 12 bags weighing each 135 pounds. What is the weight of the whole? Ans. 2820 pounds.

3. A merchant bought five pieces of linen containing 25 yards each, and 2 pieces containing 24 yards each, and 1 piece containing 26 yards. How many yards were there in the whole? Ans. 199.

SUBTRACTION AND MULTIPLICATION.

1. Multiply 342 by 22 and from the product subtract 400. Facit 7124.

2. There are 15 bags of coffee, each of which weighs 112 pounds. The bags which contain the coffee weigh 22 pounds. How much would the coffee weigh without the bags ? Ans. 1658 pounds.

3. There are 12 chests of tea, each of which weighs 96 pounds. The chests which contain the tea weigh. each 20 pounds. What would the tea weigh without the chests? Ans. 912 pounds.

DIVISION.

By division we ascertain how often one number is contained in another.

The number to be divided is called the dividend.
The number to divide by is called the divisor.

The number of times the dividend contains the divisor is called the quotient.

If, on dividing a number, there be any overplus, it is called the remainder.

The dividual is a partial dividend, or so many of the dividend figures as are taken to be divided at one time, and which produce one quotient figure.

When the divisor does not exceed 12 work by

RULE I.

Place the divisor on the left of the dividend, and see how often it is contained in the first left hand figure or figures thereof.* If it be contained an exact number of times, set down that number; and then see how often it is contained in the next figure or figures. But if it be contained any number of times with a remainder, set down the number of times, and conceive the remainder to be prefixed to the next figure of the dividend; then see how often the divisor is contained in these, and proceed as before: or if these will not contain the divisor, set down a cypher, and take the next figure with them; and if they will not still contain the divisor, set down a cypher again, and take the next figure with them; set down the number of times they contain the divisor, and proceed as before.

PROOF.

Multiply the quotient by the divisor, and to their product add the remainder (if any) and the result will be equal to the dividend.

*The multiplication table shews how often any number, not exceeding 12, is contained in any other number not exceeding 144: as that 4 is contained in 12 three times, because 3 times 4 are 12; 10 is contained in 115 eleven times with 5 over, because 11 times 10 are 110, which, with 5, makes 115.

[blocks in formation]
« ΠροηγούμενηΣυνέχεια »