2. Begin with the units and subtract each figure in the lower line from the figure over it; and set down the remainder. 3. When any figure in the lower line is greater than the figure above it, add 10 to the upper figure and from that amount subtract the lower figure and set down the remainder ; observing when you so increase the upper number by 10 always to add i to the next lower figure before subtracting, and thus proceed until the whole is finished. Proof. Add the remainder to the less number, and if the sum be equal to the greater number, the work is right. Note. The greater number is sometimes called the minuend, and the smaller the subtrahend. EXAMPLES, 1. What is the difference between 1856 and 642 ? Operation. Minuend 1856 We place the less number under the Subtrahend 642 greater; units under units, tens under tens, &c. then take 2 units from 6 units Difference 1214 leave 4 units ; and 4 tens from 5 tens leave 1 ten; and 6 hundreds from 8 hundreds leave 2 hundreds, and nothing from 1 thousand leaves 1 thousand; and the answer is 1214. 2. Subtract 528 from 873 and how many remains ? Greater num. 873 It is evident we cannot take 8 units Less number 528 from 3 units, but will suppose the upper number 3 to be increased by 10, Remainder 345 that is, we will take 1 ten off of the 7 tens, and add it to the 3 units, making Proof 873 13, and then subtract 8 from 13, leaves 5. (We have now borrowed 1 ten from the 7 tens, and in reality it is only 6 tens from which we are to subtract the 2 tens in the lower number.) We will now carry or add 1 to the next lower figure 2 tens, makes 3 tens; and 3 from 7 leaves 4. Then subtract 5 (hundreds) from 8 (hundreds) leaves 3 (hundreds) and the work is done. Note. It will be seen that carrying 1 to the lower figure 2 tens and subtracting it from the 7 tens produces the same effect; and is more convenient in practice than it would be to consider the upper figure (7 tens) from which we borrowed 1 ten; to be only 6 tens, and subtracting the lower figure, 2 tens from it ; thus, 2 from 6 leaves 4, the same as above. Hence is derived the Rule. " When the lower figure is greater than the figure above it add 10 to the upper figure,” &c. Proof. The remainder and less number added together are equal to the greater number, therefore the work is right. 3 4 Greater pumber 856 Minuend 4778 From 47784 Less number 723 Subtrahend 987 Take 4775 14. From 784656 take 645485 Ans. 139171. 15. From 913417 take 246751 Ans. 666666. 16. From 5456841 take 1209825 Ans. 4247016. 17. From 3356948 take 2468009 Ans. 888939. 18. From 479660 take 146327 Ans. 333333. 19. From 1000000 take 127653 Ans. 872347. 20. From 1225683 take 225684 Ans. 999999. 21. From three millions take one million five hundred thousand. Ans. 1500000. 22. If the minuend be 95657 and the subtrahend 84465 what is the difference or remainder ? Ans. 11192. 23. If the minuend be 1002243 and the subtrahend 667788 what is the remainder ? Ans. 334455. 24. From fifty-five thousand and thirty-six take five thousand and twenty-one. Ans. 50015; 25. Can you tell me the difference between one million and nine hundred and ninety-nine thousand ? Ans. One thousand. EXERCISES IN ADDITION AND SUBTRACTION 1. A man bought a ship for 25311 dollars, and sold her for 34728 dollars, what did he gain by the purchase ? Ans. 9417 dollars. 2. How much is 1200 greater than 365 and 721 added together? Ans. 114. 3. If I have 3541 dollars, and pay A 1200 dollars and B 975 dollars out of it, how many dollars shall I have left? Ans. 1366. 4. What number added to 9709 will make 10000 ? Ans. 291: 5. General Washington was born in the year 1732 and died in the year 1799, how old was he when he died? Ans. 67. 6. The whole population of the six New-England States in the year 1800 was 1,232,454; in 1830 it was 1,954,220 ; what was the increase in 30 years ? Ans. 721766. 7. What other numbers with these four, viz: 21, 32, 16, and 12, will make 100? Ans. 19. 8. A gentleman's whole estate amounted to eleven thousand five hundred dollars ; and he gave his two sons Charles and dward each four thousand five hundred dol. lars, and the remainder to his daughter Eliza ; what was Eliza's share ? Ans. $2500. 9. From Hartford to New York is 123 miles, thence to Philadelphia 90 miles, thence to Washington 138 miles ; now if a man travel 6 days from Hartford towards Washington, at the rate of 47 miles a day, how far will he then be from Washington ? Ans. 69 miles. 10. A wine merchant bought 843 pipes of wine for 97530 dollars, and sold 684 pipes thereof for 89631 dollars; how many pipes had he left, and what do they stand him in ? Ans. 159 pipes left, and they stand him in $7899. SUBTRACTION OF FEDERAL MONEY. RULE. Write the less number below the greater, dollars under dollars, dimes under dimes, cents under cents, &c. and subtract as in Simple Subtraction. EXAMPLES. 1. From 54 dollars 7 cents 4 Operation. $. cts. ma Greater number 54,07,4 mills, take 48 dollars 68 cents 5 Less number 48,68,5 mills. Ans. $5,3d. 8cts. 9m. or 5 dollars 38 cents 9 mills. ( Remainder 5,38,9 $ d.c. $ d.c.m. $ cts. From 54,7,8 368,4,5,6 980,00 Subtract 35,8,7 257,3,2,7 640,01 Rem. 18,9,1 $ c.m. $ C. m. From 4568,37,5 5307,73 1607,01,9 'Take 695,78,4 431,29 311,50,4 c. 8. From 135 dollars take 8 dollars 8 cents. Ans. $126,92 9. From 154 dollars 1 cent take 51 dollars 10 cents. Ans. $102,91. 10. From 348 dollars 90 cents take 158 dollars 99 cents. Ans. $189,91. 11. From 100 dollars take 99 cents. Ans. $99,01. 12. From 99 dollars 9 cents take 9 dollars 90 cents. Ans. $89,19. 13. From $50,10 take $19,01. Ans. $31,9. 14. From 783 dollars 48 cents subtract 625 dollars. Ans. $158,48. 15. From $51, take 42 cents. Ans. $50,58. 16. From 25 dollars subtract 25 cents. Ans. $24,75. 17. From 40 dollars take 40 cents 1 mill. Ans. $39,59,9. 18. From $1584,01 subtract $45,91. Ans. $1538,10. 19. Subtract 1 mill from $100. Ans. $99,99,9. 20. From 30 dollars 75 cents take 74 cents 1 mill. Ans. $30,00,9. 21. Borrowed 150 dollars, and paid 45 dollars 91 cents ; how much remains unpaid ? Ans. $104,09. 22. Charles received $135,41 and Henry received just three times as much lacking 94 cents ; how much money did Henry receive ? Ans. $405,29. 23. A man received $1500, and out of which he paid to A $511,45, to B $251,15, to C $180,39, and to D $205,98; how much had he left after paying his landlord's bill of board, amounting to 35 dollars 67 cents ? Ans. $315,36. Questions. 1. What does Simple Subtraction 5. What is this called ? Ans. borrow teach? ing 10. 2. How do you write the numbers ? How do you prove Subtraction? 3. Where do you begin to subtract? 6. What is the greater number some. 4. When any figure in the lower lino times called? is greater than the figure above it, what 7. What is the smaller number cal. would you do? When you add 10 to the led ? upper figure, what would you do with 8. What is the Rule for Subtraction the next lower figure before you sub- of Federal Money? tract it? 9. What is the sign of Subtraction ? MULTIPLICATION: ges cost ? 1. James has 5 cents, and Edward has three times as many ; How many has Edward ? 3 times 5 are how many ? 2. If 1 orange cost 5 cents, how many cents will 6 oran6 times 5 are how many y? 5 times 6 are how many ? 3. One bushel contains 4 pecks ; how many pecks are there in nine bushels ? 9 times 4=how many ? 4 times 9 are how many ? 4. At 3 dollars a yard what will 8 yards of cloth come to ? 8 times 3 are how many ? 3 times 8 are how many ? 5. At 7 dollars a barrel what will 8 barrels of flour come to ? 8 times 7 are how many ? 7 times 8 are how many ? 6. What will 4 cows come to, at 12 dollars a head ? Ans. $48. 7. Three persons purchased a garden, each paid 23 dollars ; how much did the garden cost? Ans. 69 dollars because 3 times 3 units are 9 units, and three times 2 tens are 6 tens, and 6 tens and 9 units make 69, the answer. |