Arithmetic, Oral and Written; Practically Applied by Means of Suggestive Questions

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1854 edition. Excerpt: ...and trials. Happily a correction is easily made on the slate. If, then, the remainder proves to be equal to, or greater than the divisor, the quotient figure must be too small, since the remainder shows that the divisor is contained in the partial dividend a greater number of times. On the contrary, if the product of the quotient figure and the divisor be greater than the partial dividend, it is equally evident that the quotient figure is too large. In either case the correct number must be substituted. Beginners may be materially assisted by forming a table of products of the divisor with each separate digit except the first, as in the following example, according to the contracted method. Dividend. 235 2= 470 59469805(235 Divisor factor. 3= 705 470 253063 Quotient factor. 4= 940 5=1175 1246 59469805 Proof. 6=1410 1175 7=1645 8=1880 719 9=2115 705 1480 1410 705 705 But aids of this sort should be as seldom used as possible, and when used, should be soon discontinued. Sometimes it happens, after the figure has been brought down from the dividend to the remainder, that the number is still too small to contain the divisor, as in the following example. Dividend, 80520(264 Divisor. 132 3 Part of the quotient. Here 264 was found to be contained 3 times in 805 with a remainder of 13. Bringing down the 2 from the dividend, the number 132 is found to be too small to contain the divisor. As this shows that there are no tens in the quotient, a cipher should be put in the place of tens. For, in fact, 264 goes no times in 132, and-leaves the same number (132) as a remainder. Bringing down, therefore, the last figure of the dividend (the 0), we ask how many times 264 is contained in 1320, and finding it to be 5 times, the 5 is placed as usual in the...