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what is the commmon denominator for 9, 3 27?

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3 Answers

Robert's method and answer are correct, but one can go a step further to explain to a young learner to satisfy his coriousity. First determine the LCM of 3,9,27 by factoring. 3 = 3x1 9 = 3x3x1 27 = 3x3x3x1 LCM =3x3x3x1 In solving the given problem, 2 2/9 + 6 1/3 +8 2/27 collect the whole number, and fractional parts into separate brackets to obtain( 2+6+8)+(2/9+ 1/3 + 2/27)= 16 + (2/9 + 1/3 + 2/27 ) = 16 + 1/27(3.2 +9.1 + 1.2 ) = 16 + 1/27(6+9+2)=16 17/27

Since 27 is a multiple of both 3 and 9, then 27 is the least common denominator.

     2 2/9 + 6 1/3 + 8 2/27 

In order for all the fractions to have a common denominator of 27, multiply the fraction in the first term by 3/3 and the fraction in the second term by 9/9 and leave the last fraction as is. That is, 

     (2/9)*(3/3) = (2*3)/(9*3) = 6/27

     (1/3)*(9/9) = (1*9)/(3*9) = 9/27

Replace the fraction in the first term by 6/27 and the fraction in the second term by 9/27:

     2 6/27 + 6 9/27 + 8 2/27

Add the whole numbers separately from the fractions. That is,

     (2 + 6 + 8) + (6/27 + 9/27 + 2/27) = (16) + ((6+9+2)/27)

                                                         = (16) + (17/27)

                                                         = 16 17/27

The least common denominator is the least common multiple of 3, 9, 27, which is 27.

2 2/9 + 6 1/3+ 8 2/27

= (2+6+8) + (2/9 + 1/3 + 2/27), collect integer parts and fractional parts, respectively.

= 16 + (1/27)(6+9+2)

= 16 17/27