What is the sum of the fractions 2/9, 1/4, and 1/6?

To find the sum of the fractions ( \frac{2}{9} ), ( \frac{1}{4} ), and ( \frac{1}{6} ), it's essential to first determine a common denominator for all three fractions. The denominators are 9, 4, and 6. The least common multiple (LCM) of these numbers can be calculated:

• The prime factorization of 9 is ( 3^2 ).
• The prime factorization of 4 is ( 2^2 ).

• The prime factorization of 6 is ( 2^1 \times 3^1 ).

The LCM takes the highest power of each prime:

• From 9, take ( 3^2 )
• From 4, take ( 2^2 )
• From 6, take ( 2^1 ) and ( 3^1 )

Putting these together, the LCM is ( 2^2 \times 3^2 = 4 \times 9 = 36 ).

Now, convert each fraction to have this common denominator of 36:

1. For ( \frac{2}{9} ):