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(83.) (34.) (35.) 423,674 632,153 317,232 307,316 420,432 203,671 730,248 323,680 334,263 506,213 507,325 210,600 110,897 383,734 356,237 206,341 634,156 264,871 324,563 450,071 531,634 185,174 803,463 342,106 364,230 160,705 768,342 150,176 300,430

407,821 843,204 461,007 311,289 370,679 297,313 564,735 445,168 813,792 470,334

370,432 200,406 436,216 5,338,315 Ans. 6,388,667 Ans. 621,353

(36.) 412,783 631,432 572,316 231,254 673,323 217,067 306,421 764,315 207,254 843,552 321,634 502,543 617,405 506,032 762,573

(37.) 674,326 453,403 561,734 789,867 645,275 576,182 934,922 423,641 561,232 143,671 238,406 453,762 984,651 845,359 967,423

(38.) 783,457 675,306 858,642 246,468 587,649 523,731 445,372 832,148 465,363 642,742 830,423 256,872 662,456 572,834 864,213

(39.) 863,725 755,387 964,845 836,450 645,265 783,842 532,653 6+7,412 481,735 824,364 537,572 463,489 827,343 642,536 725,342

(40.) 958,439 843,670 784,561 976,435 833,406 797,624 845,358 978,262 784,643 865,343 976,736 853,974 467,852 948,685 896,872

SECTION III.

SUBTRACTION.

Art. 25. Ex. 1. Charles having 15 cents, gave 6 conts for an orange : how many cents did he have left ?

Solution.-6 cents taken from 15 cents leave 9 cents. Therefore he had 9 cents left.

OBs. The preceding operation consists in taking a less number from a greater, and is called Subtraction. Hence,

26. SUBTRACTION is the process of finding the difference between two numbers.

The answer, or number obtained by subtraction, is called the difference or remainder.

Obs. 1. The number to be subtracted is often called the subtrahend, and the number from which it is subtracted, the minuend. These terms, however, are calculated to embarrass, rather than assist the learner, and are properly falling into disuse.

2. When the given numbers are all of the same kind, or denomination, the operation is called Simple Subtraction.

27. Sign of Subtraction (-). The sign of subtraction is a horizontal line (-), called minus, and shows that the number after it is to be subtracted from the one before it. Thus the expression 7—3, signifies that 3 is to be subtracted from 7; and is read,“ 7 minus 3,” or “ 7 less 3." Read the following: 18–7=20-9. 23-10=16--3 35-8=31-4.

Note.--The term minus is a Latin word signifying less.

QUEST.--26. What is subtraction ? What is the answer called ? Obs. What is the number to be subtracted sometimes called ? That from which it is subtracted? When the given numbers are of the same donomination, what is the operation called ? 27. What is the sign of subtraction ? Wbat does is show ? Note. What is the moaning of the term minus ?

SUBTRACTION TABLE.

2 from 3 from 4 from 5 from 2 leaves 0 3 leaves 0 4 leaves 0 5 leares 0 3 1 4 1 5 1 6

1 4 2 5 2 6 2 7

2 5 3 6 3 7 3 8

3 6 4 7 4 8 4 9

4 5 8 5 9 5 10

5 8 6 9 6 10 611

6 9 710 711 7 | 12

7 10 811 812 8 | 13

8 11 9112 913 9 14

9 12 10 / 13 1014

10 15 10

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6 from 7 from 8 from 9 from 6 leaves 0 7 leaves 0 8 leaves 0 9 leaves 0 7 1 8 1 9 110

1 8 2 9 210 2 | 11

2 9 310 311 3 | 12

3 10 4/11 4 12 4 1 13

4 11 5/12 5 13

5 14 12 6 13 6 14 6 15

6 13 7 14 715 7| 16

7 14 8 15 816 817

8 15 9 16 917 9 18

9 16 10117 10 | 18 101 19

10

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Obs. This Table is the reverse of Addition Table. Hence, if the pupil has thoroughly learned that, it will cost him but little time or trouble to learn this. (See observations under Addition Table.)

EXAMPLES.

28. When each figure in the lower number is smaller than the figure above it.

1. A farmer raised 257 bushels of apples, and 123 bushels of pears : how many more apples did he raise than pears?

n hund.

units.

1 2 3 pears.

Directions. Write the less Operation. number under the greater, so that units

may

stand under units, tens ander tens, &c., and draw a line beneath them. Beginning

2 5 7 apples. with the units or right hand figure, subtract each figure in the Rem. 1 3 4 bush. lower numvor from the figure above it, in the following manner : 3 units from 7 units leave 4 units. Write the 4 in units' place under the figure subtracted. 2 tens from 5 tens leave 3 tens; set 3 in tens' place. 1 hundred from 2 hundred leaves 1 hundred; write the 1 hundred in hundreds' place. Solve the following examples in a similar manner : (2.) (3.)

(5.) From 45

68
276

698 Take 21

56
123

453

(6.) From 54 deris. Take 3 dolls.

(7.)
76 pounds.
64 pounds.

(8.)
257 yds.
142 yds.

(9.) 325 shil. 103 shil.

10. Samuel having 436 marbles, lost 214 of them: how many

had he left? 29. When a figure in the lower number is larger than the figure above it.

11. A man borght 63 bushels of wheat, and afterwards sold 37: how many bushels had he left?

It is bvi jus tb'.t we cannot take 7 tirst Method. anits frı 13 uni's, for 7 is larger than

63 3; we therefo.e add 10 to the 3 units,

37 and it w ll raake 13 units; then 7 from Rem. 26 bu. 13 leave : 6; write the 6 in units' place under the figure subtracted. To compensate for the 10

units we added to the upper figure, we add 1 ten to the 3 tens or next figure in the lower number, and it makes 4 tens; and 4 tens from 6 tens leave 2 tens: write the 2 in tens' place

Ans. 26 bushels. We may also illustrate the process of borrowing in the following manner:

63 is composed of 6 tens and 3 Second Method. units. Taking 1 ten from 6 tens, 63=50+13 and adding it to the 3 units, we 37= 30 + 7 have 63=50+13. Separating the Rem.=20+ 6, or 26 lower number into tens and units, we have 37=30+7. Now, substracting as before, 7 from 13 leaves 6. Then as we took 1 ten from the 6 tens, we have but 5 tens left; and 3 tens from 5 tens leave 2 tens. The remainder is 26, the same as before.

30. The process of taking one from a higher order in the upper number, and adding it to the figure from which the subtraction is to be made, is called borrowing ten, and is the reverse of carrying ten. (Art. 22.)

Obs. When we borrow ten we must always remember to pay it. This may be done, as we have just seen, either by adding 1 to the next figure in the lower number, or by considering the next figure in the upper number 1 less than it is.

12. From 240 subtract 134, and prove the operation.

Since 4 cannot be taken from 0, we Operation. borrow 10; then 4 from 10 leaves 6. 1 240 added to 3 (to compensate for the 10 we 134 borrowed) makes 4, and 4 from 4 leaves 0. 106 Ans. 1 from 2 leaves 1. PROOF, -We add the remainder

Proof. to the smaller number, and since the 134 less No. sum is equal to the larger number, 106 remainder. the work is right.

240 greater No.

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