Question

Question
Simplify 6/7c − 5/9d − 1/2 c + 1/3d
.(1 point)
Responses

59c − 412d = 59c −13d
Start Fraction 5 over 9 End Fraction c minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus Start Fraction 1 over 3 End Fraction d

514c + 29d
Start Fraction 5 over 14 End Fraction c plus Start Fraction 2 over 9 End Fraction d

514c − 29d
Start Fraction 5 over 14 End Fraction c minus Start Fraction 2 over 9 End Fraction d

59c + 412d = 59c +13d

Answer 1

To simplify the expression \( \frac{6}{7}c - \frac{5}{9}d - \frac{1}{2}c + \frac{1}{3}d \), we will first combine the like terms for \( c \) and \( d \).

1. **Combine \( c \) terms:**
\[
\frac{6}{7}c - \frac{1}{2}c
\]
To combine these, we need a common denominator. The least common multiple of 7 and 2 is 14.

Convert each to have a denominator of 14:
\[
\frac{6}{7}c = \frac{12}{14}c
\]
\[
-\frac{1}{2}c = -\frac{7}{14}c
\]
Now we can combine them:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{5}{14}c
\]

2. **Combine \( d \) terms:**
\[
-\frac{5}{9}d + \frac{1}{3}d
\]
The least common multiple of 9 and 3 is 9.

Convert \(\frac{1}{3}d\) to have a denominator of 9:
\[
\frac{1}{3}d = \frac{3}{9}d
\]
Now combine:
\[
-\frac{5}{9}d + \frac{3}{9}d = -\frac{2}{9}d
\]

3. **Final result:**
Combine the \( c \) and \( d \) results:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

Thus, the simplified expression is:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

This matches the option:
\[
\text{Start Fraction 5 over 14 End Fraction c minus Start Fraction 2 over 9 End Fraction d}
\]
Therefore, the correct response is:
\[
\frac{5}{14}c - \frac{2}{9}d
\]