10. Subtract by threes, from 100 to 1; from 102 to 2; by fours, from 101 to 1; from 102 to 2; from 103 to 3.

11. Subtract by fives, from 102 to 2; from 103 to 3; from 104 to 4; from 100 to 5.

12. Subtract by sixes, from 103 to 1;

from 104 to 2; from

105 to 3; from 100 to 4; from 102 to 6.

13. Subtract by sevens, from 106 to 1; from 100 to 2; from 101 to 3; from 102 to 4; from 103 to 5; from 104 to 6; from 105 to 7.

14. Subtract by eights, from 105 to 1; from 106 to 2; from 107 to 3; from 100 to 4; from 101 to 5; from 102 to 6; from 103 to 7; from 104 to 8.

15. Subtract by nines, from 100 to 1; from 101 to 2; from 102 to 3; from 103 to 4; from 104 to 5; from 105 to 6; from 106 to 7.

From 876 take 631.

Write units under units, tens under tens, and so on. Then 1 unit

Operation. Minuend, 876 Subtrahend, 631 Remainder, 245

from 6 units leaves 5 units, and we write 5 under the units' column; 3 tens from 7 tens leave 4 tens, and we write 4 under the tens' column; 6 hundreds from 8 hundreds leave 2 hundreds, and we write 2 under the hundreds' column. The remainder, therefore, is 2 hundreds 4 tens 5 units; that is, 245.

46. The minuend is the sum of the subtrahend and the remainder. Hence, to test the accuracy of the work, add the subtrahend and remainder together, and if the work is correct, their sum will be equal to the minuend.

47. It is obvious that one number can be subtracted from another only when both numbers refer to the same things. Thus, we can subtract 3 oranges from 5 oranges, but we cannot subtract 3 apples from 5 oranges.

37.874-632. 42. 6982-5431. 47. 725,419 — 613,208. 38. 792–261. 43. 7629-4518. 48. 965,420 — 342,100.

39. 798-627. 44. 7824- 6821.

49. 854,267-723,150.

50. 549,830 – 438,820.

41. 862-741. 46. 8792-6281. 51. 628,300 - 517,200.

48. If the same number is added to the minuend and to the subtrahend, the remainder is not altered. Thus, 8-5 3; if 10 is added to 8 and to 5, we have 18 — 15 = 3; and if any number whatever is added to 8 and to 5, the difference of the results will be 3.

From 783 take 469.

Since we cannot take 9 units from 3 units, we add 10 units to the

Operation. Minuend, 783 Subtrahend, 469

Remainder, 314

3 units, making 13 units; then 9 units from 13 units leave 4 units. Now as we have added 10 units (= 1 ten) to the minuend, we add 1 ten to the 6 tens of the subtrahend, making 7 tens, and 7 tens from 8 tens leave 1 ten; 4 hundreds from 7 hundreds leave 3 hundreds. The remainder, therefore, is

3 hundreds 1 ten 4 units; that is, 314.

From 359 take 186.

Operation. Minuend, 359 Subtrahend, 186

Here 6 units from 9 units leave 3 units. Since we cannot take 8 tens from 5 tens we add 10 tens to the 5 tens, making 15 tens; then 8 tens from 15 tens leave 7 tens. Now as we have added 10 tens (= 1 hundred) to the minuend, we add 1 hundred to the 1 hundred of the subtrahend, making 2 hundreds; and 2 hundreds from 3 hundreds leave 1 hundred. The remainder,

Remainder, 173

therefore, is 1 hundred 7 tens 3 units; that is, 173.