Text-Book of Arithmetic; For the Use of Teachers Including All the Exercises in the Pupils' Manual of Arithmetic (Paperback)

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: ...of a whole number; thus, J is the reciprocal of 3; I is the reciprocal of 5. The multiplication of any number by a primitive fraction is resolvable into pure division. "Multiplication, properly so called," says Newton, "is that which is made by Integers, as seeking a new quantity, so many times greater than the multiplicand as the multiplier is greater than unity. But, tor want of a better word, Multiplication is also made use of in Fractions and Surds, to find a new quantity, in the same ratio (whatever it be) to the multiplicand as the multiplier has to unity."--Arithm. Univers., translated by Eaphson. Thus, X 4 = f X -= Vs also A X i = A; also i x fr = H The numerators and denominators of fractions, in multiplication, often admit the application of cancelling, on the principle of reduction to lower terms; thus, _3_ y 25 _ S X 8 5 _ j X 5--5, TIT ST-l0X 87 "" S X TT-The word of is often used between fractions, as an equivalent for the sign of multiplication, in which case the multiplier precedes the multiplicand. Thus, f "/ A = A X It seems needless to give such a form as f of A, the name of Compound Fraction, as many writers on Arithmetic have done. When Mixed Numbers are proposed for multiplication, the general mode of dealing with them is, first to convert them into Improper Fractions, and then to employ the operation already illustrated. But when the integral part of a given factor is large, it is generally expedient to find the entire product by means of two partial products; thus, for the 16th Exercise--8375IH x 435 = 8375 x 435 + f x 435. 8375 x 435 = 3643125-Hi X 'V = Jlo-xj = 304 Ans. 3643429 Note.--It will be useful for the pupil to recognise readily, that when a fraction is multiplied by a number equal to th...