do Hun. Tens, Units, Tenths, C. m. cts. m. cts. m. 2 6 3,6 37 65, 1 7 3 6, 8 4 3 1 6, 1 8 4 18, 0 2 1 8, 9 5 6 1 6 3, 8 1 2 1 6, 1 1 6 7, 1 6 3 6 4 0,8 0 1 8 1, 687 3, 6 3 4 310 8 4, 4 3 4 Ten in an inferiour denomination being equal to one in the next superiour, it is plain that we may add the same as in whole numbers. 4. Add 1 dollar, 65 cents and 3 mills, 5 dollars, 65 cents and 8 mills, 20 dollars, 8 cents and 4 mills, 14 dollars and 1 mill. $ cts. m. Care should be taken to supply ciphers in 1, 6 5 3 the place of vacant denominations, thus, 14 5, 6 5 8 dollars and 1 mill must be written $14,00 2 0,0 8 4 cts. 1 mill. 1 4, 0 0 1 Ans. $4 1, 39, 6 Note.-Ciphers at the right hand of decimals, or in the place of decimals, do not alter the value, therefore they may be omitted; thus, $5,00, is the same as $5. 5. Find the sum of 39 cents, 4 dimes, 5 dimes, 38 cents, 40 cents, 3 mills, 80 cents, and 2 dimes. cts. m. The student will perceive that every dime ,39 is ten cents, consequently 2 dimes make 20 cents; 3 dimes, 30 cents; 4 dimes 40 cents; ,5 0 &c. So for 2 dimes we write 20 cents, for ,3 8 3 dimes, 30 cents, and for 4 dimes, 40 cents, ,4 0 &c. ,0 0 3 6. What is the sum of 180 dols. 1 ct., 136 ,80 dols. 40 cts., 300 dols. 10 cts., 100 dols. 1 čt. ,20 1 mill. 4 dols. and 2 mills ? $3, 07 3 Ans. $720,52,3 7. A man has 5 notes, viz. : one of $36,75 cts., one of ,4 0 $84,25 cts., one of $40,80 cts, one of $101,90 cts., and one of $40,11 cts.; what is the amount of the notes ? ' Ans. $303,81 cts. 8. I received 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 cts. 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. $ 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 (1) 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 373 cts., 2 skeins of silk for 12 cts., 1 pound of tea for 373 cts. ; how much did the whole cost me? Ans. $3,371 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 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 figure 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 own the whole amount the hand co mn. set 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. Dollars 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 vacant 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 difference. Subtraction being exactly the reverse of addition, your knowledge of that rule will be of great service in this; you have alrcady 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 Melod. Add the difference between the 1 99 99 99 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 04 from 4 leaves 016 10 4 3 1/4 5. 1/6 11 5 2 4 2/4 6 6 2 3 7 37 from 7 leaves 0 2 6 44 8 417 8 1 2 7 5 9 2 2 8 6 10 67 10 3 2 9 11 717 11 2 10 814 12 817 12 5 2 11 9 5 from 5 leaves 018 from 8 leaves 0 2 12 10 5 1 3 from 3 leaves 0 5 7 2 3 4 8 3 3 5 9 4 3 6 3 10 59 from 9 leaves o 3 7 4 11 619 10 1 3 8 515 12 2 3 9 6/6 from 6 leaves 09 12 3 3 10 716 1/10 from 10 leaves 0 3 11 816 1 3 12 96 9 3/10 2 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. 2 from 4 leaves how many? how many? how ? ? ? how many? 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 ? 25 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 inany are left after taking 20 from 24 ? 6. Joseph has 16 peaches, Henry 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 had he than oranges ? 1. Examples to be performed on the Slate. From 4 6 Minuend. DEMONSTRATION.Take 3 2 Subtrahend. Commencing at the right hand as the rule directs, 1 4 Remainder or difference. we say 2 from 6 leaves 4, placing it directly under: oecause 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 difference between 46 and 32. Proof. According to the 1st method. 4 6 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 1 4 the greater. Consequently, when we add 14, the difference between 46 and 32, to 32 the less, we find the amount to be 46, $6 a number equal to the greater. Proof. According to the 2nd method. 4 6 DEMONSTRATION.- -You already understand, that the dif3 2 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 3 ? can take no more than the difference between two numbers, |