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482 HANDBOOK OF PROJECTION FOR
cannot add 4/5 and 1/3, but you could very easily add 12/15 and 5/15, and 4/5 and 12/15 and 5/15 and 1/3 have identically the same value. Before addition we, therefore, must give both fractions the same part value, which in arithmetic is called reducing them to a common denominator. Any two fractions may be reduced to a common demoniator by multiplying both factors of each fraction by the denominator of the other fraction, thus in adding 2/3 and 1/9 we would have
2 2x9 18 1 1x3 3 18 3 21
3 3x9 27 9 9x3 27 27 27 27*
SUBTRACTION.— To subtract two fractions we proceed the same as for addition, but subtract the smaller numerator
18 3 15
from the larger, thus : 2/3 — 1/9 = = — .
27 27 27
MULTIPLICATION.— To multiply a fraction by a whole number you may either multiply the numerator or divide the denominator by the whole number, as seems most expedient. The results will be the same, thus : 1/8 x 4 = 4/8 if we multiply the numerator, or 1/2 if we divide the denominator. The result is the same, because 4/8 = 1/2.
To multiply a fraction by a fraction we multiply the numerators together for a new numerator and the denominators to
3 2 3x6 6
gether for a new denominator, thus — x — = = — .
11 7 11x7 77
DIVISION — To divide a fraction by a whole number you may either divide the numerator or multiply the denominator by the whole number. The result will be the same in either
8 8-M case, insofar as has to do with value, thus : — -s 4 = =
9 9 2 8 8
— or = — , the value of 2/9 and 8/36 being the same.
9 9x4 36
To divide a fraction by a fraction you merely invert the divisor and then proceed as in multiplying one fraction by an
2 5 2 7 2x7 14 other, thus :— -5 — = — x — = = — .
3 7 3 5 3x5 15