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ARITHMETIC.
FRACTIONS.
Addition.
Fractions to be added must have a common denominator
;
thus we cannot add l
/
2 + % -f- % + U unless they be reduced
to a common denominator instead of the denominators two,
three and four ; in other words, we must find the least common
multiple of the numbers 2, 3 and 4, which is 12. Thus we
have:
i = ft
t = ft
1 3
4 = T2
3 9
4 = T2
H = 2ft = 2J
Example 2.
Add: TV + I + i + A + 1+ I + I + 1
The common denominator is found in the following
manner : Write in a line all the denominators, and divide with
the prime number, 2, as many numbers as can be divided with-
out a remainder. The numbers that cannot be divided without
a remainder remain unchanged, and these together with the
quotients of the divided numbers, are written in the next line
below. Repeat this operation as long as more than one num-
ber can be divided without remainder, then try to divide
by the next prime number, and so on. These divisors and all
those numbers remaining undivided in the last line are multi-
plied together, and the product is the least common denominator.
2) w ? i n $ n ^ 9
2) ? i 2 0374-9
2) £21 337?9
3) 211 £271?
211 11713
The common denominator is thus
:
2X2X2X3X2X7X3= 1008
Thus 1008 is the least common multiple of 16, 8, 4, 12, 7
and 9.
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