Question

Simplify 5/14a+−25c+1/8b−2/5c+3/8b+7/14a
.(1 point)

Answer 1

To simplify the expression \( \frac{5}{14}a - 25c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14}a \), we can group and combine like terms.

1. **Combine the \( a \) terms:**
\[
\frac{5}{14}a + \frac{7}{14}a = \left(\frac{5 + 7}{14}\right)a = \frac{12}{14}a = \frac{6}{7}a
\]

2. **Combine the \( b \) terms:**
\[
\frac{1}{8}b + \frac{3}{8}b = \left(\frac{1 + 3}{8}\right)b = \frac{4}{8}b = \frac{1}{2}b
\]

3. **Combine the \( c \) terms:**
\[
-25c - \frac{2}{5}c = -25c - 0.4c = -25.4c
\]
To combine \( -25c \) and \( -\frac{2}{5}c \), it's best to express both with a common denominator:
\[
-25c = -\frac{125}{5}c \quad \text{(because } -25 = -\frac{125}{5} \text{)}
\]
Now we can combine:
\[
-\frac{125}{5}c - \frac{2}{5}c = -\frac{125 + 2}{5}c = -\frac{127}{5}c
\]

Now, we put everything together:
\[
\frac{6}{7}a + \frac{1}{2}b - \frac{127}{5}c
\]

Thus, the simplified expression is:
\[
\frac{6}{7}a + \frac{1}{2}b - \frac{127}{5}c
\]