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 plus Start Fraction 2 over 9 End Fraction d

59c + 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 will first combine the terms that involve \( c \) and then combine the terms that involve \( d \).

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

- Convert \( \frac{6}{7} \) to 14 as the denominator:
\[
\frac{6}{7} = \frac{6 \times 2}{7 \times 2} = \frac{12}{14}
\]
- Convert \( \frac{1}{2} \) to 14 as the denominator:
\[
\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\]
- Now subtract the fractions:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{5}{14}c
\]

2. Combine \( d \) terms:
\[
-\frac{5}{9}d + \frac{1}{3}d
\]
Again, we need a common denominator. The least common multiple of 9 and 3 is 9.

- Convert \( \frac{1}{3} \) to 9 as the denominator:
\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\]
- Now combine the fractions:
\[
-\frac{5}{9}d + \frac{3}{9}d = -\frac{2}{9}d
\]

3. Combine the results:
So now we have:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

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

From the options presented, the closest response to \( \frac{5}{14}c - \frac{2}{9}d \) is:
**5/14c - 2/9d**