5/14a+-2/5c+1/8b-2/5c+3/8b+7/14a

Answer 1

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

1. Identify like terms:

   • Terms with \( a \): \( \frac{5}{14}a \) and \( \frac{7}{14}a \)
   • Terms with \( b \): \( \frac{1}{8}b \) and \( \frac{3}{8}b \)
   • Terms with \( c \): \( -\frac{2}{5}c \) and \( -\frac{2}{5}c \)

2. Combine like terms:

   • For \( a \): \[ \frac{5}{14}a + \frac{7}{14}a = \left(\frac{5 + 7}{14}\right)a = \frac{12}{14}a = \frac{6}{7}a \]

   • For \( b \): \[ \frac{1}{8}b + \frac{3}{8}b = \left(\frac{1 + 3}{8}\right)b = \frac{4}{8}b = \frac{1}{2}b \]

   • For \( c \): \[ -\frac{2}{5}c - \frac{2}{5}c = -\left(\frac{2 + 2}{5}\right)c = -\frac{4}{5}c \]

3. Putting it all together: Combining all the simplified terms, we have: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c \]

Thus, the simplified expression is: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c \]

Answer 2

Simplify and what’s the answer

Answer 3

Let's simplify the expression step by step again to ensure clarity:

Given expression: \[ \frac{5}{14}a - \frac{2}{5}c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14}a \]

Step 1: Combine Like Terms

1. Terms with \(a\):

   • \(\frac{5}{14}a + \frac{7}{14}a\)
   • Combine: \[ \left(\frac{5 + 7}{14}\right)a = \frac{12}{14}a = \frac{6}{7}a \]

2. Terms with \(b\):

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

3. Terms with \(c\):

   • \(-\frac{2}{5}c - \frac{2}{5}c\)
   • Combine: \[ -\left(\frac{2 + 2}{5}\right)c = -\frac{4}{5}c \]

Step 2: Write the Final Simplified Expression

Putting all the terms together: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c \]

Final Answer

The final simplified expression is: \[ \boxed{\frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c} \]

Answer 4

What the answer

Answer 5

The simplified expression of the original problem is: \[ \frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c \]

This expression cannot be simplified further without specific numerical values for \(a\), \(b\), and \(c\). Thus, the answer is the simplified expression itself:

\[ \boxed{\frac{6}{7}a + \frac{1}{2}b - \frac{4}{5}c} \]