rite an expressio $$ \frac{2}{8} b+\left(\frac{3}{8} b+\frac{4}{5}\right) $$

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UpStudy AI · Accepted Answer

Certainly! Let's start by writing and then simplifying the given expression.

### Given Expression:
$$
\frac{2}{8}b + \left( \frac{3}{8}b + \frac{4}{5} \right )
$$

### Step-by-Step Simplification:

1. **Simplify the Fractions:**
   $$
   \frac{2}{8} = \frac{1}{4}
   $$
   
   So, the expression becomes:
   $$
   \frac{1}{4}b + \left( \frac{3}{8}b + \frac{4}{5} \right )
   $$

2. **Combine Like Terms:**
   Combine the terms involving $$ b $$:
   $$
   \frac{1}{4}b + \frac{3}{8}b = \left( \frac{1}{4} + \frac{3}{8} \right )b
   $$
   
   To add the fractions, find a common denominator (which is 8 in this case):
   $$
   \frac{1}{4} = \frac{2}{8} \quad \Rightarrow \quad \frac{2}{8} + \frac{3}{8} = \frac{5}{8}
   $$
   
   So,
   $$
   \frac{1}{4}b + \frac{3}{8}b = \frac{5}{8}b
   $$

3. **Write the Simplified Expression:**
   $$
   \frac{5}{8}b + \frac{4}{5}
   $$

### Final Simplified Expression:
$$
\frac{5}{8}b + \frac{4}{5}
$$

### Optional: Combining into a Single Fraction
If you prefer to have the expression as a single fraction, you can find a common denominator for the two terms:

1. **Determine the Least Common Denominator (LCD):**
   The LCD of 8 and 5 is 40.

2. **Rewrite Each Term with the LCD:**
   $$
   \frac{5}{8}b = \frac{5 \times 5}{8 \times 5}b = \frac{25}{40}b
   $$
   $$
   \frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}
   $$

3. **Combine the Terms:**
   $$
   \frac{25}{40}b + \frac{32}{40} = \frac{25b + 32}{40}
   $$

### Combined Single Fraction:
$$
\frac{25b + 32}{40}
$$

You can choose to use either form based on your preference or the requirements of your specific application.
The simplified expression is $$ \frac{5}{8}b + \frac{4}{5} $$.

rite an expressio \( \frac{2}{8} b+\left(\frac{3}{8} b+\frac{4}{5}\right) \)

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