Rational arithmetic Author:Sarah Porter This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1852 Excerpt: ...them into common fractions, in order to operate upon them; thus, you will find it easier to multiply-by = than to mul o 7 tiply.3333, &c, ... more »by.142857;--it is, therefore, useful to know how to change readily a recurring decimal into a common fraction of the same value. If, instead of marking the strip of paper into tenths, I had marked it into ninths, we should then have had no difficulty in dividing the whole into 3 equal parts, since the ten tenths could be divided into 3 parts, having one over, it follows that 10--1 could be divided into 3 parts without leaving any remainder. In like manner, if the paper had been marked into 999999 parts, these could have been divided by 7 without a remainder, since we have found that 1000000-4-by 7 = 142857, and one over, it follows that 1000000-1 = 999999 can be divided by 7 without a remainder, each part being 3 1 142857. Therefore-is the same as decimal.3 =-, by dividing denominator and numerator by 3, and 142857 1-the same as.142857 =-, by dividing; numera 999999 7' J tor and denominator by 142857. What has been said above shows that the same reasoning will equally apply to any other recurring decimal. Therefore, speaking generally, any recurring decimal is truly represented by a fraction, the numerator of which is the repetend, and the denominator 9, repeated to as many places as there are figures in the repetend. When it is a mixed decimal--that is, when the recurring part does not commence immediately, such as.7954;.8673; then, by breaking the numbers into frac 79 54 79 54 54 tions, we have.7954 =.= m and; but-xa x m §x io5 = ni; therefore m + 6 79 x 11+6 875 = reduced to its lowest 1000 3000 3000 3000 (52) Bring. 8563 into a fraction (53) Also.76117. (54) Also 2428571. (55) Also 5909. PART THIRD. COMMERCIA...« less