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1. Suppose a farm to produce 340 bushels of wheat, 1746 bushels of corn, 233 bushels of oats: what is the whole product of the farm?
Ans, 2325. 2. Suppose you freight a boat with 143 barrels of iour, 75 barrels of potatoes, 106 barrels of pork, and 56 barrels beans: how many barrels would you then have on board?
Ans. 380. 3. A gentleman left his sons 3600 dollars, his daughters 1375 dollars, his grand children 570 dollars, the American Bulle Society 4600 dollars, the Orphan Asylum 500 dollars: what was the amount of his estate?
4. Money was first made of gold and silver at Argos, 894 before Christ: how long has money been in use at this date, 1828?
Ans. 2722. Add together the following numbers: six hundred and thirty, one thousand four hundred and thirteen, seven thousand eight hundred and twenty, four hundred and seventy five.
Ans. 10338. 6. From the Creation to the departure of the Israelites from Egypt was 2513 years; to the siege of Troy 307 years," to the building of Solomon's temple 180 years; to the building of Rome 251 years; to the destruction of Carthage 607 years; to the death of Julius Cæsar 102 years; to the Christian era 44 years: what was the time from the Creation to the Christian era?
QUESTIONS. a What is Simple Addition? b How do you place numbers to be added? c Where do you begin the addition? d How is the amount of each column to be set down! e How is addition proved? f Why do you carry by ten?
SIMPLE SUBTRACTION. A Simple Subtraction is taking a less number from o greater of the same denomination, thereby showing the difference.
b. The greater number is called the minuend, the less number the subtrahend, and the difference, the remainder.
c Place the less number under the greater, with units under units, tens under tens, &c. Then, beginning at the right hand, or place of units, take each lower figure from the one above it, and set down the difference. When d] the figure in the lower line is greater than the one above it, suppose 10 to be added to the upper figure, and take the difference of their sum; but in this case, you must add 1 ta the next figure in the lower line. This is called borrow ing ten.
e Note. The reason why borrowing ten, and carrying one to the next lower figure, does not affect the difference, is plain from the fact, that the one is added to the next higher place in the subtrahend, which is equal to ten in the lower.
f Add the remainder and subtrahend together, and if their sum correspond with the minuend, the work is supposed to be right.
EXAMPLES. 1.7649654 2. 347638476 3. 34563041 Minuend.
3426143 238476564 16742963 Subtrahend. 4223511 109161912 17820078 Remainder, 7619651 347638176 31563041 Proof.
APPLICATION, 1. How long since the discovery of America by Columbus in 1492?
336 years, Ans. 2. A Merchant deposited in Park 7645 dollars, and drew out 4245 dollars: how much remained? Ans. 3400.
Suppose'a man's income to be 640 dollars a year, and his expenditures 435 dollars: how much does he save?
Ang. 205. 3. How long from the discovery of America by Columbus in 1492, to the declaration of Independence in 1776?
years. 4. A owes B 475 dollars, and pays of this sum 260 dollars: what sum remains due?
Ans. 215. QUESTIONS. a What is Simple Subtraction? B What are the given numbers called? c How must they be placed?
d When the figure in the lower number is greater than the one in the upper, what is to be done?
e How does it appear that borrowing ten, in subtracting a less number from a greater, does not affect the difference? f How is subtraction proved?
SIMPLE MULTIPLICATION. a SIMPLE MULTIPLICATION teaches, having two numbers given of the same denomination, to find a third, which shall contain either of the two given nun
rs as many times as the other contains a unit; as 6 multiplied by 4, or 4 times 6 5) are 24. The given numbers spoken of together are called c] Factors ; separately, the first or largest number is called Multiplicand, and the other Multiplier; the amount or numd] ber sought is called the Product.
Before any desirable progress can be made in this rule, which is considered the most important one in Arithmetick, the following Table must be rendered perfectly familiar to The mind.
-116 2021123/32 36 40 441 18
| 25 30|35| 10451 50 55 60 6
3642|48 154 | 601 661 72 7
44915663 | 70 | 771 84 8
#64172 | 81 | 897 90 9
781 | 901 99 108 10
100 110 120 111
11211132 12 I have given the Table in this form, because I am convinced by long experience, that it will be more readily committed to memory.
Find the smaller of the two numbers in the left hand column, and the larger one at top, and in the square on a line with the one, and under the other, their product will be found. Thus the product of 6 and 8 is 48; so 5 times 7 are 30; 4 times 6 are 24.
To commit the table to memory, begin with the second line from the top: Thus, twice 2 are 4; twice 3 are 6; twice 4 are 8, &c. Then the second; 3 times 3 are 9; 3 times 4 are 12, &c.
e 1. Place the numbers as in Subtraction, the less under the greater, with units under units, &c. and draw a line below them.
f 2. When the Multiplier does not exceed 12: begin at the right hand of the multiplicand, and multiply each figure contained in it, carrying by ten as in addition.
g 3. When the Multiplier erceeds 12: multiply by each figure separately, first by the units, as directed above, then h] by the tens, &c. always placing the first figure of each product directly under the figure by which you multiply; having, in this manner, gone through with each figure in the multipiier, add the several products together, and their sum will be the product required.
1. Multiply 5362 by 4. The numbers being placed as seen
Operation in the Example, say 4 times 2 are 5362 8, which set down under the mul.. 4 tiplier 4: then 4 times 6 are 24; set
down 4 and carry 2. Again 4 times
21448 3 are 12, and two to carry are 14; then 4 times 5 are 20, and 1 to carry are 21, which set down, and the work is done. 2. What is the product of 3256 multiplied by 56 5 Factors 3256 Multiplicand.
19536 Product by the unit figure, (or 6.) 16280 Product by tens, (or 5.)
182336 Product or answer.
PROOF. i The better way of proving multiplication is, to divide the product by the multiplier, and if the work be right, the j] quotient will correspond with the multiplicand: or cast the nines out of each of the factors separately; and set their remainders at the right and left of a cross, as above; multiply the figures thus placed together, and cast the nines out of their product, and place the remainder at thetop of the