Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[ocr errors]
[ocr errors]

(3) CCC.

(5) XXX. R. (1) II.

(7) CC.
(2) XX.
(1) MM.

(6) MMM. S. (1) VI. (6) VIII.) (11) CV.

(16) DCL.
(2) XI.
(7) XII.
(12) CX.

(17) DCCCLX.
(3) LI.

(8) LIII. (18) XVI. (:8) MCCLIII.
(1) CI.
(9) XV.

(11) CXV. (19) MDCLXXIII. (5) VII. (10) LX.

(15) DCCX. T. IV. 1 1 IX. | (3) XL / XC. (CM (CD.

(8) LIX.

(5) CIX. U. (1) XIV.

(7) DXC.
(2) XIX.
(4) CIV.
(0) CXL.

(8) MCD.
XXVI. (5) LXXXVI. (0) CCCXL.
(2) XXXVII. (R) CCXXVIII. (10) DCLIX.
(3) LXVII. (7) DCCXVI. (11) DXCIX.
(1) LXXV.
(8) CCIV.

(12) MDCCXLIV. W. (1) I. (3) X. >> XIX. LIV.

(9)

CCXIX. (2) L. (4)VI. (6) XXXVII. (XC. (10) DXLVIII.

[ocr errors]
[ocr errors]
[ocr errors]

(1)

X. (1)

(19) 178.

147

17:

Express in Roman numerals :

(13)
4.
13.

45.
(2)
(8)
(14)

(20)
7.

58.
(3)
(9)

(21)
3.
14.

(15) 69.

(25) 699. () 1567. (27) 1643. (38) 1729.

2 10. (1C)

(22) 19.

IIO. 235. (5) (11) (17)

(28)
9.
23.

150. 367.
(12)
(18)

(24) II 34.

165. 544.

(1) 6.

(16)

(20) 1868.

CHAPTER II.

ADDITION.---SECTION I.

The object of addition is to unite two or more numbers into one. Thus, if John has 4 marbles and James 3, they will have 4 and 3, or seven marbles between them. The number 7 is called the sum of 4 and 3, and the operation by which it is found is called addition.

We will begin with the most simple case, namely, the addition of two or more numbers of one figure.

If we are required to add the numbers 5 and 3, we may hold up three fingers, and counting from 5, say six, seven, eight; the sum is 8.

Again, if we wish to add the numbers 4, 2, and 3, first hold up two fingers, and counting from 4, say five, six; 6 is the sum of 4 and 2 ; now hold up three fingers, and counting from 6, say seven, eight, nine ; 9 is the sum of 4, 2, and 3.

Examples.-Apply this method to find the sum of the following numbers :-A. 5 and 2.

3, 4, and 5.
3
and
4.
(11) 8 and 6. 6, 4, and

5.
4
and
5. 5 and 7.

4, 8, and 6.
7 and 2.

9
and 8.

7, 9, and 3.
3 and 2.

7 9. 8, 7, and 5.
4
and
3. 9

and

9. 9, 8, and 5. 5 and 4.

(1)

(17)

(9) 8 and 2. (10) 6 and 5.

(2)

(18)

5, 2, and 6.

(3) 6 and 3.

(10)

(1)

(12)

(20)

(5)

(18)

(21)

(15)

and

(22)

[ocr errors]

4, 3, and 2. The above process may be followed in finding the sum of any two or more numbers of one figure ; but if the pupil will learn the addition table, which contains the sum of any two numbers of one figure,

(18)

(8)

(10)

(24)

7, 9, and 8.

he will be able to perform the operation more readily, as follows :

Add together 2, 4, 8, and 3.

2

4 8 3 17

Set down the figures under one another, and say 3 and 8 are 11, 11 and 4 are 15, 15 and 2 are 17.

SECTION II.

Addition of a number of one figure to any number of two figures.

Find the sum of 18 and 7.

Since 18 is i ten 8 units, if we add 7 units, we get i ten 15 units, or 2 tens 5 units, that is 25. In the same way it may be shown that 28 and 7 are 35; 38 and 7... 45; 68 and 7... 75; 88 and 7...95, and so on.

The pupil should practise exercises like these :6 and 7 are 13, 16 and 7...23, 26 and 7...33 ; 9 and 8 are 17, 19 and 8... 27, 29 and 8... 37, 59 and 8...67, 79 and 8...87, and so on.

SECTION III.

Addition of any numbers whatever.

Rule.—Place the numbers under one another in such a manner that units may stand under units, tens under tens, hundreds under hundreds, and so on, and draw a horizontal line under the last row of figures. Add up the figures in the first column on the right hand, set down the units figure in their sum, and carry the tens (if any) to the next column ; proceed in the same manner till the last column is added, when both the units and tens (if any) must be set down.

Proof.—- The accuracy of the addition may be tested by adding the columns downwards as well as upwards. Examples. --Add together 5387, 4639, 584,

6357, 78. 5387

Placing the numbers under one 4639 another, according to the rule, we

584 add the figures in the units column 6357

thus-8 and 7 are 15, and 4 are 19, 78 and 9 are 28, and 7 are 35, that is, 17045

35 units, or 3 tens 5 units; set the 5 under the units figures, and carry

the 3 tens to the column of tens. Beginning with the 3 carried, we say 3 and 7 are 10, and 5 are 15, and 8 are 23, and 3 are 26, and 8 are 34, that is, 34 tens, or 3 hundreds 4 tens; set the 4 tens under the tens' figures, and carry the 3 hundreds to the hundreds' column; adding this in the same manner, we find the sum to be 20, that is 20 hundreds, or 2 thousands o hundreds, put o in the hundreds' place (because if we do not the next figure will be taken for hundreds instead of thousands), and carry 2 thousands to the thousands' line; proceeding as before, we find the sum to be 17, that is, 17 thousands, and this being the last column, we set down 17.

The following sign + is sometimes used to express the addition of two or more numbers, and is read plus, or more by. The words is equal to, or equals, are usually denoted by two parallel straight lines thus=. Hence 5+7=12 is read 5 plus 7 equals 12. B. 324 '432

432 231 143 432 134 124 213 423 413 234 213

132 402

(3) 312

(5)543

16) 134

213

(3) 534

(6) 354

(5) 463

(9)

264

D. (1375

0) 538

(3) 647

(

(6) 768

456 387

(10) 487

(7)
(8)
(9)

(16)
435

314

406 204 402

23 310 340 324 502 231 )

(1)

(5) 243

342 432 435 424 243 435 563 543 243 342 235 244 246 264

(10) 545

543

342
324
547

436
436 365 357 274

584 (R) 675
643 674 354 637 384
467 238 268 584 758
1645
(8)

(0)

584 486

678 678 378

387 E. (1)653

547 478 689

476 589 608 480 639 375 589

759

596 (7)

(8)

748
489 697 589 769
573 979

497

896 F. (1) 3867

(3)

(5) 7468

3804 4538 3726 3754 3846 675 2645 4537 2673

758 2408 3726 2865 5746 4652

397 (8)

(10) 389

5867 286 4680 5647

8409

989 5174 97

806 759

7895
389

593
6084

4907

568 478 536

786

(2) 574

(3) 6922

(1) 476

(0)597

958

[merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]
« ΠροηγούμενηΣυνέχεια »