Simplify 6/7c - 5/9d -1/2c + 1/3d
A. 5/9c+4/12d=5/9c+1/3d
B. 5/14c+2/9d
C. 5/9c-4/12d=5/9c-1/3d
D. 5/14c-2/9d
To simplify the expression, you'll want to combine like terms. The like terms here are those with the variable c and those with the variable d. Let's combine them:
For the c terms:
\( \frac{6}{7}c - \frac{1}{2}c \)
To combine these, you need a common denominator. The smallest common denominator for 7 and 2 is 14. Therefore, you convert each fraction:
\( \frac{6}{7}c = \frac{12}{14}c \) (after multiplying top and bottom by 2)
\( \frac{1}{2}c = \frac{7}{14}c \) (after multiplying top and bottom by 7)
Now subtract them:
\( \frac{12}{14}c - \frac{7}{14}c = \frac{5}{14}c \)
For the d terms:
\( \frac{-5}{9}d + \frac{1}{3}d \)
The smallest common denominator for 9 and 3 is 9. So you convert the fraction with the denominator of 3:
\( \frac{1}{3}d = \frac{3}{9}d \) (after multiplying top and bottom by 3)
Now subtract them:
\( \frac{-5}{9}d + \frac{3}{9}d = \frac{-2}{9}d \)
Combine the simplified c and d terms:
\( \frac{5}{14}c - \frac{2}{9}d \)
So the correct answer is:
D. \( \frac{5}{14}c - \frac{2}{9}d \)