Rule.—Find the least common multiple of the given denominators for a common denominator. Then for each new numerator take such a part of this common denominator as the fraction is part of 1.
Reduce 1⁄2, 2⁄3 and 3⁄4 to their L. C. D.
Work: 12 = 612 23 = 812 34 = 912
Ans. 6⁄12, 8⁄12 and 9⁄12.
The L. C. M. of the denominators 2, 3 and 4 is 12. Hence, 12 is the L. C. D. to which the given fractions can be reduced. Then to change 1⁄2 to 12ths, say, 1⁄2 of 12 is 6, and write it over 12; to change 2⁄3 to 12ths, say 2⁄3 of 12 is 8, and write it over 12; to change 3⁄4 to 12ths, say, 3⁄4 of 12 is 9, and write it over 12.
Fractions must be reduced to a common denominator to be added or subtracted.
Addition of Fractions
If two or more fractions have the same denominator, their sum is obtained by adding the numerators.
Work: 17 + 47 + 57 = 1 + 4 + 57 = 107 = 137
If the fractions have different denominators, we must first express them as equivalent fractions with the same denominator.