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noughts from the right of the divisor and as many figures from the right of the dividend and divide in the usual way; if there be a remainder place on the right of it all those figures which were cut off from the dividend.

Examples.--Divide 38 1759 by 7000.

The factors of 7000 are 1000 and 7. Dividing by 1000, we get a quotient 381 and remainder 759; 7)381

and now dividing by 7 we 759

get a quotient 54 and re54 3

mainder 3, multiplying this remainder by 1000, the first divisor, and adding the first remainder we get the complete remainder, 3759.

In practice the division is performed as follows :7.000)381,759

Cut off the three noughts

in the divisor and three 54 3759

figures from the dividend; divide 381 by 7, the quotient is 54 and remainder 3 ; now place after 3 the figures cut off in the dividend and we get the complete remainder 3759 as before.

Divide-
R. (1) 38759 by 20.

137594 by 6o.
39475 by 30.

23750 by 70. (3) 62590 by 40.

351794 by 80. (9) 16357 by 50.

2319750 by 90. L. (1) 473865 by 300.

1237590 by 6000. 517396 by 500. 3857496 by 9ooo. 381794 by 2000. (8) 14379605 by 800oo. 659370 by 3000. 4137658 by 1100. 743957 by 700.

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31745968 by 12000.

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SECTION V.
Division of any two numbers whatever.

Divide 98735 by 31. Here the dividend is 98 thousands 7 hundreds 3 tens 5 units ; now 31 is contained in 98 three times with remainder 5, and therefore in 98 thousand 3 thousand times with remainder 5 thousand or 50 hundred, adding the 7 hundred in the dividend, we get 57 hundred; now 31 is contained in 57 once with remainder 26, and therefore it is contained in 57 hundred 1 hundred times with remainder 26 hundred or 260 tens; adding the 3 tens in the dividend we get 263 tens, and since 31 is contained in 263 eight times, with remainder 15, therefore it is contained in 263 tens 8 tens times with remainder 15 tens or 150 units, lastly adding the 5 units in the dividend we get 155 units and 31 is contained in this number 5 units times without remainder.

Hence the quotient is 3 thousands i hundred 8 tens 5 units, or 3185.

The above process may be expressed thus :31)98 th. 7 hn. 3 tns. 5 uts.(3 th. í hn. 8 tens. 5 uts.

93 th.

5 th. 7 hn.
or 57 hn.

3 hn.

26 hn. 3 tis.
or 263 tns.

248 tns.
15 tns, 5 uts.

or 155 uts.

155 uts,

In practice the denominations of the figures are omitted and the division is generally performed as follows : 31)98735(3185 Write the divisor to the 93

left of the dividend, and the 57

figures of the quotient as they 31

arise to the right, and draw 263

lines to separate the divisor 248

and quotient from the divi

dend. 155

Since the divisor is not 155

contained in the first figure

of the dividend, we take the number 98 formed by the first two figures ; now 31 is contained in 98 three times, therefore we put 3 for the first figure of the quotient and multiply the divisor by this quotient figure ; 3 times 31 is 93, which subtracted from 98 leaves 5; to this remainder we bring down 7, the next figure of the dividend, this makes 57, and 31 is contained in it once with a remainder; put i for the second figure of the quotient, and subtract 31 from 57, this leaves 26; to this remainder bring down 3

the next figure in the dividend, this makes 263, and 31 is contained in it 8 times with a remainder ; put 8 for the third figure of the quotient, 8 times 31 is 248, and this subtracted from 263 leaves 15; lastly bring down 5 from the dividend, this makes 155, and 31 is contained in it 5 times; 5 times 31 is 155; subtracting, there is no remainder. Hence the quotient is 3185 as before.

Divide 244126597 by 4600o.

Cut off three noughts in the divisor and three figures in the dividend and divide 2441 26 by 46 ; the quotient is 5307 and the remainder 4 ; bring

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326

M. (1)

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(0) 6958 by 71.

(2) 861 by 41.

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46,000)244126,597(5307 down the figures cut

off in the dividend and 230

we get 4597 for the 141

complete remainder.

When the work is

expressed in full, as in 322

the above examples, the 4597

operation is called Long Division, but when the multiplication and subtraction are performed mentally the quotient only being set down, the operation is called Short Division. Examples.-Divide341 by 31. 1395 by 31.

3233 by 61. (10) 6097 by 91. 1173 by 51. 4544 by 71.

1394 by 41. 4758 by 61. N. 7533 by 31.

43168 by 71. 17442 by 51.

34587 by 61. 14924 by 41.

58138 by 82. 24583 by 61.

76360 by 92. 38340 by 71.

50499 by 93. 0. (1) 14706 by 43

(6) 19584 by 34. (2) 28275 by 65.

(7) 63640 by 86. (3) 26936 by 74

78473 by 97. (1) 46410 by 85.

(0) 28083 by 37. (5) 66364 by 94.

51861 by 59. P. (1) 1495582 by 314. (6) 6131985 by 865.

2481741 by 423. 8400432 by 976.
2021724 by 534. (8) 4365060 by 547-
4119701 by 643.

(0) 6322064 by 658.
4362644 by 754 6987903 by 769.

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Q." 26725704 by 564. (6) 56569086 by 807.

(2) 18520588 by 478. (7) 6436902 by 186.
(5) 38419595 by 685. (8) 16839485 by 295.

59626768 by 796. 31366 176 by 397.
52034073 by 897.

(10) 14701764 by 196. R.(1) 548216938 by 752. 98124184 by 752. 2067083 by 581.

(7) 82 1675282 by 492. 38734836 by 588. (8) 1536821396 by 372.

913806034 by 758. (0) 140168432 by 158. (5) 1869123124 by 872. (10) 182166492 by 916. S. (1) 123759486 by 2300.

541730065 by 19000. 123115375493 by 34000. 100300056 by 59000.

26583795 by 5300. 410310080 by 43700. (163748650 by 39000. 283174000 by 28300.

385467003 by 4700. 6753000oo by 179000. T.

73043578 by 3124. I 83015584 by 3472. (2) 1413684212 by 8152. 5456279296 by 9472. (3) 483368748 by 8374. (8) 792168434 by 7904. (1) 195291798 by 6550. () 1345687228 by 7748. (5) 740788506 by 2966. 1482127684 by 4986.

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EXAMINATION PAPERS.

A. 1. Express in words 15, 38, 70, 63 ; and in figures fourteen, twenty-three, fifty, eighty-seven.

2. Add together 5, 4, 3, 8; and find the sum of 14, 9, 23, 7, 28. 3. Find the difference between 257 and 538. 4. Multiply 47362 by 6, and 58479 by 7. 5. Divide 972 by 4 and 2124 by 6.

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