Simplify 6/7c − 5/9d − 1/2 c + 1/3d

Question

.(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