7^3--7^^^-7-^r3- (^^



FRACTIONS. 29

Commencing now with the expression y of |- : we know
that -f means 5 times one-seventh ; therefore, if I have to
take five-sevenths of any quantity, I first take ow^-seventh
of it, and then multiply the quot* obtained by 5 : i. e, to
take 7" of |-, I must divide the |- by 7, and multiply it by
5 : hence, according to our rules of mult** and div** of fractions
by whole numbers, I multiply the den' of the •§■ by 7, and
the num' by 5, and have

7 3 7x3 ^ '

Comparing (F) and (G), I now perceive that

5-252
-of- = _ X —.
7 3 7 3

54. The following explanation may, perhaps, be intelligible to some
pupils :

In multiplying a quantity, whether whole or fractional, by a whole
number, I repeat that quantity as many times as there are units in the
multiplier :

Thus, 7 X 5, or 7 times 5, means that I am to repeat the 5 as many
times as there are units in 7 ;

So, 7 X t shows that I am to repeat §, as often as there are units in 7 ;

Also, 1 X t shows that I am to repeat f as often as there are units in 1,
t. e. 1 time, or once :

Therefore, | X § ought to mean, that I am to repeat f as often as there
are units in |.
