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20. Nannie brought 6 pears to school, and gave 2 of them

to her teacher. How many had she left?

21. How many are 15 apples less 8 pears?

We cannot take 8 pears from 15 apples. For 15 apples = neither 7 pears nor 7 apples. Hence,

8 pears

73. Only abstract numbers, or like concrete numbers, can

be subtracted.

22. From 9 tens take 2 ones.

We cannot take 2 ones from 9 tens. For 9 tens

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74. Only like orders of units can be subtracted.

Written Exercises

CASE I.

75. When each figure in the Subtrahend represents a less value than the corresponding figure of the Minuend.

EXAMPLE.-From 68759 subtract 37422.

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We now subtract each figure of the subtrahend from the figure above it in the minuend, writing each result in the remainder. 2 ones from 9 ones leave 7 ones; 2 tens from 5 tens leave 3 tens; 4 hundreds from 7 hundreds leave 3 hundreds ; 7 thousands from 8 thousands leave 1 thousand; 3 ten-thousands from 6 ten-thousands leave 3 ten-thousands.

The result, 31337, is the difference or remainder.

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8. Bought 30

them for $5999.

9. A owns 8 has A than B?

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?

Ans. 5391.

Ans. 24203.

Ans. 513140.

6.68754-5521 = ?

7. 190856 100203

=?

shares of bank stock for $3789 and sold How much did I gain?

horses and B owns 4. How many more

After each has bought 4 more, how many more has A than B? Hence,

76. When the same number is added to both minuend and subtrahend, it does not change their difference.

Written Exercises

CASE II.

7. When a figure in the Subtrahend represents a greater value than the corresponding figure of the Minuend.

EXAMPLE. From 54 subtract.19.

SOLUTION.

Minuend, 54
Subtrahend, 19
Remainder, 35

EXPLANATION.-It is evident that we cannot subtract 9 ones from 4 ones. But by adding 10 ones to the minuend and 1 ten (10 ones) to the subtrahend (76), we can perform the subtraction very readily. 5 tens 14 ones. 2 tens

54 = 5 tens 4 ones; add 10 ones and we have 19 1 ten 9 ones; add 1 ten and we have

=

9 ones.

3 tens

5 ones,

And 2 tens 9 ones from 5 tens 14 ones =
or 35, the required difference or remainder.

EXAMPLE. From 924 take 376.

SOLUTION.

924

376
548

EXPLANATION.-We write the numbers as in the margin and say mentally :

6 ones from 4 ones impossible; but 6 ones from 14 ones leave 8 ones. Since we added 10 ones (1 ten) to the minuend, we must add 1 ten (10 ones) to the subtrahend. 7 tens and 1 ten are 8 tens; 8 tens from 2 tens impossible; but 8 tens from 12 tens leave 4 tens. added 10 tens (1 hundred) to the minuend, we must add 1 hundred (10 tens) to the subtrahend. 3 hundreds and 1 hundred are 4 hundreds; 4 hundreds from 9 hundreds leave 5 hundreds. Result, 548.

Since we

78. RULE.—Write the subtrahend so that its units shall stand under the units of the same order in the minuend. Begin at the right-hand and subtract from each figure of the minuend the corresponding figure of the subtrahend and write the remainder underneath.

If in the minuend any figure expresses a less number of ones than the corresponding figure of the subtrahend, add 10 to the former; then subtract, and add 1 to the next figure of the subtrahend. Proceed thus till the work is complete.

79. PROOF.-When the work is correct, the sum of the remainder and subtrahend equals the minuend.

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24. By the P. R. R. the distance from Pittsburgh to New York is 444 miles; from Pittsburgh to Philadelphia, 355 miles. What is the distance from Philadelphia to New York? Ans. 89 miles.

25. By the same road, from Pittsburgh to Harrisburg is 246 miles. What is the distance of Harrisburg from Philadelphia? From New York? 1st Ans. 109 miles.

2d Ans. 198 miles.

26. Washington was born A. D. 1732, and died in A. D. 1799. How old was he at his death? Ans. 67 years.

27. The sum of two numbers is 20560; the less is 3745. What is the greater? Ans. 16815.

28. A merchant sold on Saturday goods amounting to $2567; on Monday goods amounting to $1075. What is the difference in the two days' sales? Ans. $1492.

29. If a man's property is valued at $15725, and his debts at $6837, what is he worth?

Ans. $8888.

30. If a man's property is valued at $20569, and his debts

at $30880, what excess of debt has he?

Ans. $10311.

31. A man sold a horse for $375, making $97. How much did the horse cost him?

Ans. $278.

32. A and B together bought property for $275315, and A furnished $98676 of the purchase money. How much did B furnish? Ans. $176639.

33. America was discovered by Columbus in 1492. How many years had elapsed in 1837? Ans. 345 years.

34. I deposited in the bank $1840, and drew out $475. How many dollars had I left? Ans. $1365.

35. A man has property worth $10104, and owes debts to the amount of $7426. When his debts are paid, how much will he have left? Ans. $2678.

36. A man having $100000, gave away $11. How many dollars had he left? Ans. $99989. 37. A man bought a span of horses for $537 and a yoke of oxen for $297. How much more did he pay for the horses than for the oxen? Ans. $240.

38. A man having $8795 gave $2309 of it for a store. How much money had he left?

Ans. $6486.

39. A merchant owing $35542 paid $22560. How much does he still owe? Ans. $12982. 40. A merchant selling goods at $6789, gained $444. What did they cost? Ans. $6345.

41. Chatham is 47 miles west of York, and Howe is 91 miles west of York. How far is it from Howe to Chatham? Ans. 44 miles.

42. If the distance of the moon from us is 240000 miles, and that of the sun 95000000 miles, how much farther is it to the sun than to the moon? Ans. 94760000 miles.

43. Washington died A. D. 1799, at the age of 67. In what year was he born? Ans. 1732.

44. At an election the successful candidate received 5075 votes, and had a majority of 387 over the defeated candidate. How many votes did the latter receive?

Ans. 4688 votes.

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