A Familiar Explanation of the Higher Parts of Arithmetic

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. 1848 edition. Excerpt: ... In working this Ex. we shall first reduce the former of the given quantities to the fraction of the latter, and then convert into a decimal the vulgar fraction connecting the two quantities. 4s.6jd. _ 54Jd. _ J09 _ 13-625 1 240d. 480 60 2-270833 MISCELLANEOUS EXAMPLES. 126. The same remark applies to these Miscellaneous Examples in Decimals that applied to the corresponding Exs. in Fractions: and the only general assistance that can be given to a pupil is to show him the neatest method of performing the operations required. Ex. I. B 3. Multiply 8 17s. 6d. by 75-25, and reduce the result to the decimal of 100. Here ( l?s-6d.) X (75-25) _ 8X7525 100 100 _ 8-875x75-25 100 = 667-84375 ouLut" c ' " wof & T drto a Moving the point three places to the right in two numerators and in two denominators, and again one place to the right in the numerator and the denominator of the second fraction, the expression becomes 131-yJlyWyA--131 m W U aW_9x6xllX3 si, m 3 9 a _ 11-90909.... 9x6x3 _ 1-32323232 6X3 _-22053872053872 3 =-07351290684624, &c. Since a very large number of decimals is non-terminating, it might seem that vulgar fractions, which are always expressed in finite terms, would be preferable for every purpose. But this is not the case, for decimals have one advantage over fractions from the following consideration. In ascertaining the comparative value of two or more fractional quantities, if they be expressed as vulgar fractions, it is necessary to reduce them to a c. D.; but if they are represented as decimals, mere inspection will detect their comparative value, as readily as can be done in whole numbers. For example, if we have to compare-rV, -5-5-, -j- -, we cannot see...