86. These, of course, consist of questions involving
one or more of the Cases which we have considered;
and all that can be done towards guiding the pupil in
such Ess. 10, merely to aaast ^uaii m v^^^^%



58 FRACTIONS.
what operations are required in solving any proposed
question.
What was said in Case XI. applies more particularly
here^ viz., that it is necessary most carefidly to note the
sign*, or rather the words which express signs. As an
example of this caution^ I will consider A 4 ; and in order
to work it, I shall endeavour to see what operations are
intended by the words employed in the question. The
sum is as follows :

Multiply the sum of ■§-, |- of 4-, and 4, by l\i.
Now, the sum of means addition, or (+), and of means
( X ); therefore, this Ex. expressed in signs is (-§-+1- x-|-+4)
X 71i- This is now in the form of an Ex. under Case XI.,
and the remaining work may be completed by a pupil.
87. B 5. How many persons may receive each 3f s. out
of £13^?

This is only a Reduction sum, involving fractions ; and,
in plainer language, means — ^how often are 3|^s. contained
in £13* ? or, if I divide £13* by 3*s., what is the
quotient ?

£13}



The quotient required is



3#s.
69 20s.
_ 13}x20s. 5 1

3|s. ~ 23



(U)



= 4x^X-l=72

By (67) we know that the second fraction in line (U)
will be an abstract number ; and the result, 72, shows that
3j^s. are contained 72 times in £13*.
