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FRACTIONS.
Multiplication.
Fractions are multiplied by fractions, by multiplying numer-
ator by numerator and denominator by denominator ; thus
:
I X Ta = 96 — 3’2
The correctness of this rule can easily be understood if
we consider these two fractions as two problems in division,
t X ft will then be 3 divided by 8 and the quotient multiplied
by 7 and the product divided by 12; thus, 3 is to be multiplied
by 7 and the product is to be divided by 8 times 12. Therefore :
3X7 IX
8
8 X X? 8X4 iZ
A mixed number may first be reduced to an improper frac-
tion and then multiplied as a common fraction, numerator by
numerator and denominator by denominator. For instance
:
^i X | = j X f = x — 2f
A fraction may be multiplied by a whole number by multi-
plying the numerator and letting the denominator remain un-
changed. For instance :
Ax2 = it = iA = ii
This must be correct, because we may consider 7 as indicat-
ing the quantity and 12 as indicating what kind of quantity in
exactly the same sense as we may say 7 dollars or 7 cents ; if
either of those were multiplied by 2 the product would, of
course, be either dollars or cents respectively, and for the same
reason 7 twelfths multiplied by 2 must be 14 twelfths.
A fraction may also be multiplied by a whole number, by
dividing the denominator by the number and letting the numer-
ator remain unchanged. For instance :
ft X 2 = | — 1|, because ft is equal to |, so must ft X 2
Examples.
No. 1. 3i X f = V X | = ||
No. 2. \\ Xli = |X f = f = 2X
No. 3. ft X \ — ft
No. 4. 14Xft = 3
i
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