Question

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

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

5/9c + 4/12d = 5/9c +1/3d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d

5/9c − 4/12d = 5/9c −1/3d
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

5/14c + 2/9d

Answer 1

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

### Step 1: Combine the \( c \) terms

First, we will combine \( \frac{6}{7}c \) and \( -\frac{1}{2}c \):

- The least common multiple (LCM) of 7 and 2 is 14.
- Convert \( \frac{6}{7} \) to a fraction with a denominator of 14:
\[
\frac{6}{7} = \frac{6 \times 2}{7 \times 2} = \frac{12}{14}
\]
- Convert \( -\frac{1}{2} \) to a fraction with a denominator of 14:
\[
-\frac{1}{2} = -\frac{1 \times 7}{2 \times 7} = -\frac{7}{14}
\]

Now combine:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{12 - 7}{14}c = \frac{5}{14}c
\]

### Step 2: Combine the \( d \) terms

Next, we will combine \( -\frac{5}{9}d \) and \( \frac{1}{3}d \):

- The least common multiple of 9 and 3 is 9.
- Convert \( \frac{1}{3}d \) to a fraction with a denominator of 9:
\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\]

Now combine:
\[
-\frac{5}{9}d + \frac{3}{9}d = \frac{-5 + 3}{9}d = -\frac{2}{9}d
\]

### Final Expression

Combining both simplified terms, we get:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

So the simplified expression is:

\[
\frac{5}{14}c - \frac{2}{9}d
\]

Thus, the correct response is:
**\( \frac{5}{14}c - \frac{2}{9}d \)**.