$84,25 cts., one of $40,80 cts., one of $101,90 cts., and $40,11 cts.; what is the amount of the notes? one of Ans. $303,81 sta 8 Treceived of A, B, and C, the following sums: A paid me $140,50 cents, B $500,58 cents, C $1000; can you tell me how much I received from the three? Ans. 1641,08 ets. 9. A paid me $300, B paid me $400, and C paid me as much as A and B both, what did they all pay me, and what did I receive from C ? They all paid me $1400. I received of C {$700. 10. A man has four farms, one is worth $2000, one $2560, one $1206, and one $5600; what is the worth of the four? Ans. $11366. NOTE-Where half (3) cents occur, it is evident that every two halves make a whole; you will then add one to the cents for every two halves; thus in the eleventh sum, we have 3 halves, that is, one cent and a half, so you will write down the half and add one to the cents.And it is also evident, where a half is given to find the whole, that the half twice repeated or added will equal the whole; one third (1) three times repeated will equal the whole; and one fourth (1) four times repeated will equal the whole, 11. Bought 5 gallons of molasses for $2,50 cts., 2 pounds of coffee for 37 cts., 2 skeins of silk for 12 cts, 1 pound of tea for 37 cts.; how much did the whole cost me? Ans. $3,37 cts. 12. One half of a vesse is worth fifteen hundred dollars; what is the whole worth? Ans. $3000. 13. One third of a man's estate is in land which is worth $2000; what is his whole estate? Ans. $6000. 14. If a man receive one thousand dollars for one quarter () of his property; what should he receive for the whole? Ans. $4000. QUESTIONS ON SIMPLE ADDITION. What is simple addition A. Collecting several numbers in one. What is the number called that a t arises from the operation of the work? A. Sum or amount How do you place your numbers for adding ? A. Units under units, tens under tens, &c. Where do you commence adding? A. At the right hand. How do you proceed in the work A. Add the right hand column, and write down the right hand figur of the amount under the column added, and add the left to the first figure of the next column; and so proceed through all the columns, remembering to set down the whole amount of the left hand column. How do you prove addition? A. By adding the columns downwards. Why should that prove it? A. It is putting together the same numbers that composed the first amount, only in a different order. How do you write down Decimal or Federal money for adding? A. Døllars under dollars, cents under cents, and mills under mills. After your numbers are written down, how do you proceed in adding ? A. The same as in whole numbers. Why do you add the same? A. Because one in a superiour column, is equal to ten in the next inferiour column, the same as in whole numbers. In federal money what are the figures called at the left hand of the separatrix? A. Dollars.— What are the two next at the right called? A. Cents. What is the next at the right called? A. Mills. If a denomination be wanting "what do you write in its place? A. A cipher or ciphers to fill the va cant places. Do ciphers at the right hand of a decimal alter its value? A. They do not. When you have the value of a half given, how do you find the value of the whole? A. Add the given sum to itself, and the amount will be the value of the whole. If you have the value of one third given, how do you find the value of the whole ? A. Set down the value of the third three times, and add; the sum will be the value of the whole SIMPLE SUBTRACTION, Is taking a less number from a greater. The greater number is called the Minuend, and the less the Subtrahend. The number produced from the operation of the work is called the remainder or dif ference. Subtraction being exactly the reverse of addition, your knowledge of that rule will be of great service in this; you have already learned by addition that 4 and 3 make 7; and now you will readily perceive that if either be taken away from 7, the other will remain. You also understand that addition is collecting numbers together; you must now learn that subtraction is taking them apart. RULE-Place units under units, tens under tens, &c. as in addition, with the greater number above. Draw a line under them.Begin at the right hand, and subtract the units of the subtrahend from those of the minuend, and write the difference directly below. Proceed in like manner with the remaining figures at the left. But if a figure in the subtrahend exceed that above it in the minuend, you must add 10 to the upper figure, and from the amount take the figure below; remembering to add 1 to the next figure of the subtrahend; this is adding equals to both the given numbers, for the convenience of work; and adding equals to both numbers, their difference must ever remain the same. Subtraction is denoted by a horizontal line; thus, 6-3-3 signifies that the difference between 6 and 3 is 3. PROOF. 1st Method. Add the difference between the given numbers to the subtrahend, and if the amount equal the minuend, the work is right. 2nd. Method. Or you may subtract the difference from the minuend, and if the remainder equal the subtrahend, the work is right. SUBTRACTION TABLE. 2 from 2 leaves 014 from 4 leaves 016 10 19 2222 NNN N-222 8 9 10 11 12 5 3 15 14 5 16 11 6769012 8 5 from 5 leaves 018 from 8 leaves 0 " n The student should be required mentally to answer the following questions. If there be a class, let each student answer his question directly after reading it. 1. John having 9 cents, paid 6 cents for apples; how many had he left? 2. George having 11 oranges, gave 4 to his mother; how many had he left? P 3. A man paid 15 dollars for a cow, and sold her for 20 how much did he gain by the trade? 4. Charles bought a knife for 15 cents, but soon became sick of his bargain, and sold it for 12 cents; how much did he lose? 5. Charles gave Henry 24 cents, George gave him 20; how many did Charles give more than George? How many are left after taking 20 from 24? 6. Joseph has 16 peaches, Henty 4, and George 24; how many has George more than the other two? 7. Henry bought an English Reader for 30 cents, and a writing book for 20; but George offers for his writing book what his English Reader cost him; how much will Henry gain by selling? 8. Charles carried 24 eggs to market, and sold them for 8 oranges; how many more eggs had he than oranges? 1. Examples to be performed on the Slate. From 46 Minuend. DEMONSTRATION:Commencing at the right hand as the rule directs, 14 Remainder or difference. we say 2 from 6 leaves 4, placing it directly under: because it is plain if 2 units be taken from 6 units, there will remain 4 units. Then we say 3 from 4 leaves 1, placing it directly under; for it is evident, if 3 tens be taken from 4 tens, there will remain' 1'ten; consequently we have 14 for the dik ference between 46 and 32. 4 6 PROOF. According to the 1st method. DEMONSTRATION. Nothing can be more plain, than the proof 32 of this rule. Because it is clear, that it can take no more than the difference between two numbers, to make the less equal to 14 the greater. Consequently, when we add 14, the difference between 46 and 32, to 32 the less, we find the amount to be 46, 4 6 a number equal to the greater. PROOF. According to the 2nd method. 4 6 DEMONSTRATION.You already understand, that the dif 32 ference between two numbers when added to the less, gives a sum equal to the greater, and you will now readily perceive, 14 that if the difference between two numbers be taken from the greater, it must leave a number equal to the less. Because it 32 can take no more than the difference between two numbers, ... when taken from the greater, to diminish it, so that it shall be equal to the less; for you perceive, when we take 14 from the minuend, it is reduced to 32, a number equal to the subtrahend. Consequently subtraction may be made to prove itself. NOTE. We might very properly have offered subtraction, as a proof of addition, had you been acquainted with the rule. It is a saying of the school boy, that it is a poor rule that will not work both ways. We have already proved subtraction by addition; then to make the rule good according to the test of the school boy, we will prove addition by subtraction. Let 46 and 32 be added, the amount is 78; now it is plain, if the numbers which compose this amount, be taken away, nothing will be left; thus, if from 78 you subtract 46, the first number, 32, will remain; and if 32, the other number, be taken away from 32 the remainder, nothing will remain. Now you may treasure up in your mind this fact; that if you subtract from the amount of any sum the several numbers that compose the amount, you destroy it or reduce it to nothing. 2. From 4 2 Take 24 In this example, we find that the 4 units of the subtrahend cannot be taken from the 2 in the minuend; therefore we add 10 to the 2, which increases it 18 to 12; then we say, 4 from 12 leaves 8, placing it under. Then we add 1 to the 2, the next figure of the subtrahend, which increases it to 3; we then say, 3 frora 4 leaves 1, placing it directly under, which leaves 18 for the difference of the 2 given numbers. DEMONSTRATION. The reason of this operation is plain when we recollect that the 1 ten which we add to the subtrahend is equal to the 10 units which we add to the minuend; because one in a superiour column is equal to 10 in an inferiour column; and adding equal sums to two numbers, or subtracting equal sums, the difference between the two numbers must ever remain the same; thus, 1 5+1 0 2 5-6=1 9 1 2+1 0-2 2-=1 6 NOTE. Adding 10 to a figure in the minuend before we can subtract, and then one to the next left hand figure of the subtrahend, is by some called borrowing. 3. Again, to show the principles of this rule in a different, though, if possible, in a clearer light, we introduce the following example. From 5 4 (39) DEMONSTRATION.-When no figure in the subtrahend is greater than that directly above it in the minuend, the student finds no difficul28 difference. ty. And even when a figure in the subtrahend is greater than that directly above it in the minuend, the difficulty vanishes, when he properly understands the local value of numbers. In this example our minuend (54) consists of 5 tens and 4 units; and our subtrahend (26) consists of 2 tens and 6 |