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Ex. 2.

From 6053 take 5846

Here, as I cannot subtract 6 from 3, I borrow 10 and add to the 3, which makes 13; then I say, 6 from 13 leaves 7, which I set down. Rem. 207 Then I carry 1 to the 4, (on account of the 10 which I borrowed,) and say, 1 to 4 is 5, and Proof, 6053 5 from 5 leaves 0, which I set down. Then, 8 from 0 I cannot, but, (I borrow 10, and then say,) 8 from 10 leaves 2, which I set down. Then, 1 carried to 5 is 6, and 6 from 6 leaves 0; and, as there are no more figures to the left, I do not set down the 0, because ciphers at the left hand of whole numbers are useless.

Note.-In Simple Subtraction, when it is necessary to borrow, instead of adding the 10 borrowed to the upper figure, and then subtracting the lower figure from the sum, as directed in the foregoing Rule, you may, if you choose, subtract the lower figure from 10, and add the remainder to the upper figure, and set down the sum below: then carry 1 to the next figure in the lower number; and so proceed.

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Ans. 40910.

12. From seventy-four thousand and twenty, take thirtythree thousand one hundred and ten.

13. From eighty thousand, subtract five hundred and eight. Ans. 79492.

14. From two hundred and twenty-eight thousand, take two hundred and twenty-eight. Ans. 227772.

15. Subtract one from a million, and show the remainder. Ans. 999999.

PRACTICAL QUESTIONS.

1. If a man's yearly income amounts to 2950 dollars, and his expenses to 2400 dollars, how much is added to his estate yearly? Ans. 550 dollars. 2. A owes Bone thousand and five dollars: If eight hundred and seventy dollars of this debt should be paid, how much would then remain due? Ans. 135 dollars.

3. A vinter bought 20 casks of wine, containing in all 1260 gallons; and afterwards sold 14 casks, containing 948 gallons: How many casks, and how many gallons of wine had he left? Ans. 6 casks, and 312 gallons. 4. A owes B 756 dollars, and Cowes B 1273 dollars; how much does C's debt exceed A's?

Ans. 517 dollars. 5. The city of Philadelphia was founded by William Penn, in the year 1683: how many years from that time to the year 1831! Ans. 148 years.

6. Homer, the famous Greek epic poet, died about 900 years before the birth of Christ, and Virgil, the prince of the Latin poets, died 19 years before Christ: How many years from the death of Homer to the death of Virgil ? Ans. 881 years.

7. Gunpowder was invented by Roger Bacon, in the year 1280; how long was this before the invention of printing by Laurentius of Harlem, which was in the year 1430? Ans. 150 years.

8. In the year 1820, the State of Connecticut contained 275248 inhabitants; Rhode-Island 83059; New-Hampshire 244161; Maine 298335; and Vermont 235764. The city of London, in the same year, contained a population of about 1225000 souls: How many more inhabitants were there in London than in the five States above mentioned ? Ans. 88433.

9. The number of inhabitants in the whole world is supposed to be about six hundred and fifty millions: About

two hundred and seventeen millions of them are professors of Christianity; one hundred millions are Mahometans; three millions are Jews; and the rest Heathens: What is the number of Heathens, and how many more Heathens are there than Christians?

Ans. The number of Heathens is 330 millions, and there are 113 millions more Heathens than Christians.

QUESTIONS ON THE FOREGOING.

1. What is subtraction? 2. What is the greater number called? 3. What is the less number called? 4. What is their difference called? 5. What is simple subtraction? 6. When you would subtract one number from another, how do you set them down? 7. Where do you begin to subtract; and how do you proceed? 8. What is to be done when any figure in the lower number is greater than that above it? 9. How is subtraction proved?

MULTIPLICATION,

Is a compendious method of performing Addition; teaching how to find the amount of any given number when repeated a certain number of times; as 3 times 4, which is 12; that is, 4 repeated 3 times, (viz. 4+4+4,) makes 12.

The number to be multiplied, or repeated, is called the Multiplicand; the number to multiply by, or the number of repetitions, is called the Multiplier; and the number produced by multiplying the former by the latter, being the total amount of all the repetitions, is called the Product. Also, the multiplicand and multiplier are both called Factors.

SIMPLE MULTIPLICATION,

Is the multiplying of any two or more numbers together, without having regard to their signification; as 4 times 5 is 20.

Before proceeding to any operations in multiplication, it is necessary to learn very perfectly the following table of all the products of the first 12 numbers, commonly called the multiplication table,

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6 12

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90-99108

7 14 21

18 | 24 | 30 | 36 | 42 | 48 | 54 2835 | 42 | 49 | 56 | 63 8 16 24 32 40 | 48 | 56 | 64 | 72

72 81

9|18|27|36| 45 | 54 | 63 10 | 20 | 30 | 40 | 50 | 60 | 70 |80| 90 | 100 | 110 | 120 |11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132| 12 24 36 | 48 60 | 72 | 84 | 96 |108| 120 | 132 | 144|

To commit this table to memory, begin with the 2 in the top line of figures, and multiply each figure in the left hand column by it, and you will find each product in the 2d column right against the figure you multiply; thus, twice 1 is 2, twice 2 is 4, twice 3 is 6, and so on. Then take the 3 in the top line for a multiplier, and multiply each figure in the left hand column by it, as before, and you will find the several products in the 3d column, against the figures you multiply; thus, 3 times 1 is 3, 3 times 2 is 6, &c. In like manner proceed through all the columns in the table, and each product will be found in the same column with the multiplier, right against the multiplicand.

CASE I.

To multiply any number by a single figure, or by any number not greater than 12.

RULE.

1. Set down the multiplier under the right hand figure, or figures, of the multiplicand, and draw a line underneath.

*The invention of this table is ascribed to Pythagoras, a Grecian philosopher, who died about five centuries before the birth of Christ. The table is formed by addition, in the following manner: The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, are written in the first column; then each of these numbers is added to itself, and the several sums are written in

2. Multiply the right hand figure of the multiplicand by the multiplier; if the product is but one figure, set it down in the place of units below the multiplier; but if it consists of more figures than one, set down only the right hand figure of it, and carry, the rest to be added to the product found by multiplying the next figure of the multiplicand.

3. Multiply the next figure of the multiplicand by the multiplier; to the product add the number,(if any,) carried from the former product; set down the right hand figure of the sum, and carry the rest, (if any,) to be added to the product in the next place, as before; and so proceed in multiplying all the figures of the multiplicand by the multiplier, and set down the whole amount found in the last place at the left hand.†

EXAMPLES.

L. Multiply 30256 by 4.
Operation.

Multiplicand, 30256) The
Multiplier, 4 Factors.

Product,

121024

Explanation. I first place the multiplier under the right hand figure of the multiplicand, and draw a line underneath. Then I begin at the right hand to multiply, and say 4 times 6 is 24; I set down 4 and carry 2: then, 4 times 5 is 20, and the 2 I carried makes 22; I set down 2 and carry 2: then, 4 times 2 is 8, and the 2 I carried makes 10; I set down 0 and carry 1: then, 4 times

the 2d column, which contains each number in the first column doubled. Each number in the first column is then added to the number standing against it in the 2d column; and the several sums are written in the 3d column, which contains each number in the first tripled; and in this manner the table is formed throughout.

+ The reason of this rule is the same as for the process in Addition, in which 1 is carried for every 10, to the next place, gradually as the several products are produced one after another, instead of setting them all down one below another, as in the annexed example.

8742
6

12- 2×6 240= 40x6 4200 700×6 48000-8000×6

52452-8742×6

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