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47. 87342+741986+8431+73298+87679+75986+85

3765+74967+93426+3843.

48. 1741+-87394+17396+73983+29664+79865+234

67+52484+69421+8493.

49. 638423+1753846+395843+6604241+8493+8789 +213245+338006+74294+22408+67542+817540+758 50. 6741986+444876+222999+6078546+839423+83 88966+321486 +1753948+173982+842123+948663+23. 942884.

51. Add together, eight thousand and ninety-six; nine thousand and one; seven thousand one hundred and eighteen; seven thousand eight hundred and twenty-five; and thirty-four thousand and forty-nine.

52. Add together sixty-four thousand, one hundred and sixteen; ninety-four thousand, eight hundred and ninety-six; fifty-eight thousand, seven hundred and ninety-four; eight hundred and thirty-six thousand, and forty-seven; five hundred and forty-eight thousand, nine hundred and ninety-nine; and eleven thousand four hundred and thirty-six.

Let the following Examples be added without placing the umnbers under each other, but, commencing at the right-hand, add the units of each sum together regularly from right to left, placing the first figure of the total at a convenient distance, to make room for a figure or two more than the greatest number of figures in any of the given sums to be added; then adding the tens of the amount of the units thus found, to the tens in the first right-hand row which hath tens, add them as before from right to left, which will give a second figure of the total; thus proceed until all the rows are added. Between the last given number and the total amount, place two small parallel lines thus which is the sign of equality.

= 296.

53. 47+20+81+64+73+11
54. 73+95+67+184+300+75 =
55. 85+78+96+33+87+93.

56. 1000+739+984+673+8491.

57. 1874+1763+ 1934+1081+1231.
58. 7548+6594+849+10000+945.

59. 67191+4020+8473+8968+4709+4814.
60 41684+21419+648+64075+85+438+6571+

37842+850+495+7824.

Should the teacher wish for more examples in this form, let the pupil dispose of any of the preceding in the same manner and thus add them, which will be another method of proof.

SUBTRACTION.

SUBTRACTION teaches to find the difference between two numbers, by taking the less from the greater.

The greater number is called the Minuend, the less the Subtrahend, and the answer or number found, the Remainder. This character-Minus, is used to denote subtraction, and is always placed before the number to be subtracted: thus, 9-4 signifies, that the number 4 is to be subtracted from the number 9; which being done, the result is 5. Here 9 is the minuend, 4 the subtrahend, and 5 the answer or remainder.

From the greater of two given numbers of the same denomination, to subtract the less, take the following

RULE.

Beginning at the right-hand, subtract each figure of the less number, from its corresponding figure in the greater, and set down the several remainders.

When the figure of the subtrahend is equal to the corresponding figure of the minuend, the remainder or difference is nothing, for which a cipher must be set down. Ciphers, when they are all together or single, on the left-hand side of the significant figures, as they do not in such place increase or diminish a number, may be wholly omitted.

When the digit to be subtracted, is greater than its corresponding digit in the minuend, add 10 to the latter figure, and from the sum take the figure to be subtracted; set down the remainder, and carry one to the next figure on the left-hand in the subtrahend, and proceed as before.

The remainder added to the subtrahend, will produce a total equal to the minuend, if the work is right; or the remainder subtracted from the minuend, will give another remainder equal to the subtrahend, which affords two methods of proof.

DEMONSTRATION.

When the figures in the minuend are all greater than those in the subtrahend, it matters not in what order they are subtracted. They might, in such case, be subtracted from right to left, or in any other order; but if any digit in the minuend be less than its corresponding digit in the subtrahend; for example, if we had to subtract 286 from 564, we cannot subtract 6 units from 4 units; nor 8 tens from 6 tens; we may, in such case suppose the minuend resolved into parts of 400, 150,

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