The simplified value of `[ 5/8 - ( 5/8 - ( 5/8 - 3/8)}]` of `3.6 - 0.8 div 10` is :

Options

A. 0.88
B. `-0.82`
C. `-0.88`
D. `0.82`

Answer

To solve the expression \[ 5/8 - (5/8 - (5/8 - 3/8)) \] and then evaluate \[ 3.6 - 0.8 \div 10 \], we will break it down step by step.

### Step 1: Simplify the innermost bracket
We start with the innermost expression:
\[ 5/8 - 3/8 \]

Calculating this:
\[ 5/8 - 3/8 = (5 - 3)/8 = 2/8 = 1/4 \]

### Step 2: Substitute back into the expression
Now, we substitute \( 1/4 \) back into the expression:
\[ 5/8 - (5/8 - 1/4) \]

### Step 3: Simplify the next bracket
Now we simplify \( 5/8 - 1/4 \):
First, convert \( 1/4 \) to have a common denominator with \( 5/8 \):
\[ 1/4 = 2/8 \]

Now calculate:
\[ 5/8 - 2/8 = (5 - 2)/8 = 3/8 \]

### Step 4: Substitute back into the outer expression
Now we substitute \( 3/8 \) back into the expression:
\[ 5/8 - 3/8 \]

### Step 5: Final calculation
Calculating this gives:
\[ 5/8 - 3/8 = (5 - 3)/8 = 2/8 = 1/4 \]

### Step 6: Evaluate the second part of the expression
Now we evaluate \( 3.6 - 0.8 \div 10 \):
First, calculate \( 0.8 \div 10 \):
\[ 0.8 \div 10 = 0.08 \]

Now substitute this back into the expression:
\[ 3.6 - 0.08 \]

Calculating this gives:
\[ 3.6 - 0.08 = 3.52 \]

### Step 7: Combine the results
Now we have two results:
1. From the first expression, we have \( 1/4 \) which is \( 0.25 \).
2. From the second expression, we have \( 3.52 \).

### Final Result
The final simplified value is:
\[ 0.25 \text{ and } 3.52 \]