67. To subtract when one or more terms of the subtrahend are greater than the corresponding terms of the minuend.

68. There are two methods of explaining this case, called the Method of Borrowing and the Method of Adding Ten. We will solve the same problem by both methods.

1. From 836 subtract 472.

OPERATION. 836

472

364

SOLUTION BY BORROWING.-We write the subtrahend under the minuend, and begin at the right to subtract. 2 units from 6 units leave 4 units, which we write under the units; we cannot take 7 tens from 3 tens, we will therefore take 1 hundred from the 8 hundreds, and add it to the 3 tens; 1 hundred equals 10 tens, which, added to 3 tens, equals 13 tens; 7 tens from 13 tens leave 6 tens, which we write in tens place; 4 hundreds from 7 hundreds (the number remaining after taking away 1 hundred) leave 3 hundreds, which we write in the hundreds place.

SOLUTION BY ADDING TEN.-2 units from 6 units leave 4 units; we cannot take 7 tens from 3 tens, we will therefore add 10 tens to the 3 tens, making 13 tens; 7 tens from 13 tens leave 6 tens; now, since we have added 10 tens, or 1 hundred, to the minuend, our remainder will be 1 hundred too large; hence to obtain the correct remainder we must add 1 hundred to the subtrahend; 1 hundred and 4 hundreds are 5 hundreds; 5 hundreds from 8 hundreds leave 3 hundreds.

Rule.-I. Write the subtrahend under the minuend, plac ing terms of the same order in the same column, and draw a line beneath.

II. Begin at the right and subtract each term of the subtrahend from the corresponding term of the minuend, writing the remainder beneath.

III. If any term of the subtrahend is greater than the corresponding term of the minuend, add 10 to the latter, and then subtract.

IV. Add 1 to the next term of the subtrahend (or subtract I from the next term of the minuend), and proceed as before. Proof. Add the difference to the subtrahend; and if the work is correct the sum will equal the minuend.

SECOND METHOD.-Subtract the difference from the minuend, and if the work is correct, the result will equal the subtrahend.

NOTE.-The taking one from a term of the minuend is called borrowing, and the adding one to the next term of the subtrahend is called carrying.

32. From one million and one, take three thousand and three. Ans. 996998.

33. From four hundred thousand take four hundred and forty-four. Ans. 399556.

34. From seventy-seven thousand take seven thousand and seventy-seven. Ans. 69923. 35. From one hundred million and one take one million and five. Ans. 98999996. 36. From 6 billion, 6 million, 6 thousand and 6, take 80 million, 80 thousand and 8. Ans. 5925925998.

MENTAL EXERCISES.

1. Mary bought 20 apples and gave Ella 6 of them; how many did Mary then have?

SOLUTION.-If Mary bought 20 apples and gave Ella 6 of them, Mary en had the difference between 20 apples and 6 apples, which is 14 apples. 2. A boy found 16 eggs in the barn and broke 8 of them; how many remained unbroken?

3. How many birds will escape if I shoot 6 birds out of a flock of 40 birds?

4. How many are 17 less 8? 14 less 9? 21 less 7? 23 less 67 25 less 8? 31 less 4?

5. How many are 32 less 3? 41 less 2? 50 less 6? 49 less 7? 73 less 8? 100 less 9? 124 less 12?

6. Required the value of 112 minus 8; 120 minus 7; 125 minus 8; 132 minus 5; 140 minus 4; 150 minus 5; 150 minus 10.

7. A boy having 12 apples, bought 6 more, and then sold 8; how many had he then?

8. Mary having 14 cents, spent 8 cents, after which her father gave her 12 cents; how many cents had she then?

9. Edwin had $24 and earned $6, and then spent $12; how much did he then have?

10. A merchant gave $65 for goods, and paid $6 for transportation; at what price must he sell the goods to gain $12?

11. Subtract 36 from 84.

SOLUTION.-30 from 84 leaves 54, and 6 from 54 leaves 48.

12. Subtract 26 from 42; 35 from 52; 38 from 60; 42 from 75; 45 from 72; 48 from 84; 52 from 86; 56 from 82.

13. Subtract 123 from 147; 135 from 248; 152 from 285; 206 from 456; 307 from 444; 328 from 565.

14. In a school numbering 75 pupils 28 are absent; how many pupils are present?

15. A lady bought a watch for $250 and sold it at a loss of $35; what did she receive for it?

16. A man bought a horse for $175, paid $15 for his keeping, and sold him for $240; what was the gain?

17. A lady bought some needles for 8 cents, some thread for 15 cents, and some tape for 18 cents, and hands the clerk a 50-cent note: what is her change?

18. A man went into a clothing store and bought a vest for $6, a coat for $25, and a pair of pants for $12; he hands the clerk 5 ten dollar bills; what change will he receive?

19. Count by 6's from 6 to 72 and back; from 5 to 77 and back from 4 to 76 and back; from 3 to 75 and back; etc.

20. Count by 7's from 7 to 84 and back; from 6 to 90 and back from 5 to 89 and back; from 4 to 88 and back; etc.

21. Count by 8's from 0 to 96 and back; from 1 to 97 and back. from 2 to 98 and back; from 3 to 99 and back; etc.

22. Count by 9's from 0 to 108 and back; from 1 to 109 and back from 2 to 110 and back; from 4 to 112 and back; etc.

23. Take the number 12, add 3, subtract 2, add 4, subtract 3, add 5, subtract 4, add 6, subtract 5, add 7, subtract 6, and name the result 24. How many are 12 plus 8, minus 7, plus 10, minus 6, plus 12, minus 9, plus 14, minus 18, plus 25, minus 16?

25. How many are 25 plus 20, minus 16, plus 36, minus 40, plus 56, minus 25, plus 72, minus 84, plus 120, minus 140?

WRITTEN EXERCISES.

1. A man had 725 bushels of wheat and sold 367 bushels; how many bushels remained?

SOLUTION.-If a man had 725 bushels of wheat and sold 367 bushels, there remained the difference between 725 bushels and 367 bushels, which is 358 bushels.

OPERATION.

725

367

358

2. A farmer raised 627 bushels of potatoes, and sold 386 ushels; how many bushels remained? Ans. 241 bushels. 3. From a farm containing 3075 acres, 2528 acres were sold; how many acres remained? Ans. 547 acres.

4. A man borrowed $3052 and afterward returned $2527; how much does he still owe? Ans. $525.

5. A sold his house for $2572, which was $285 more than it cost; how much did it cost? Ans. $2287.

6. Two men together have $5682; how much money has the first if the second has $3826?

Ans. $1856.

7. A man bought a farm for $10,852, and sold it at a loss

of $987; what did he receive for it?

8. A and B together own 10,840 acres does B own if A owns 5284 acres?

9. Gen. Zachary Taylor was born in 1850; how old was he when he died?

Ans. $9865. of land; how much Ans. 5556 acres. 1790 and died in Ans. 60 years. in 1774 and died Ans. 69 years.

10. Robert Southey was born at Bristol in 1843; how old was he at his death?

11. Socrates was born at Athens 468 years before Christ, and died 398 years before Christ; what was his age at death? Ans. 70 years.

12. Walter Scott was born in the year 1832; how old was he at his death?

1771, and died in Ans. 61 years. Milton in 1608 to

13. How many years from the birth of he birth of George Washington in 1732? Ans. 124 years. 14. A farmer having 478 cows, sold 198 of them, and then bought 226; how many had he then?

Ans. 506.

15. How many years from the birth of William Penn in 1644 to the birth of Benjamin Franklin in 1706?

Ans. 62 years.