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IO .FRACTIONS.
Division.
A fraction is divided by a fraction by writing the fractions
after each other, then inverting the divisor (that is, changing
its numerator to denominator and its denominator to numer-
ator), proceed as in multiplication. For instance
:
5 _i_ 3 — 5 V •* 20 5
8 • 4 T X 3 24 6
The reason for this rule can very easily be understood,
when we consider the fractions as problems in division. That is
to say, 5 shall be divided by 8 and the quotient is to be divided
by one-fourth of 3. But if the quantity f is divided by 3 instead
of one-fourth of 3, we must, of course, multiply the quotient by
4 to make the result correct. Therefore :
8-4 o
2 _l_q 20 5.
"8" •
d 24 6
A fraction may be divided by a whole number by dividing
the numerator by the number and letting the denominator re-
main unchanged. For instance :
9 _i_ q — 3
T6 • ° T6
A fraction may be divided by a whole number by multiply-
ing the denominator by the whole number and letting the
numerator remain unchanged. For instance :
Mixed numbers are reduced to improper fractions the
same as in multiplication ; they are then figured the same as if
they were proper fractions.
Examples.
No 1 -7- — i -7- y 2 14 — 7
1NU. 1. 16 .
2 16 A : 16 8
Nn 9 -5- — & — _5_ v 4 — 20 — io
1MO. Z. is . 4 18*3 54 27
Vf n q oi _i_ 1 l — U v 3 — 51
No. 4. 2i ~ 6 = | -f- 6 = TV
No. 5. 3i -f- 4 — -U -5-4=|
In No. 4 it will be understood that f divided by 6 must be
f¥, because T\ is exactly a sixth of J.
In No. 5, also, it will be understood that if V1 is divided by
4, the quotient must be f, because 4 is one-fourth of 16.
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