Convert ` 15(17)/(40)` into a decimal fraction.

Answer

To convert the mixed fraction \( 15 \frac{17}{40} \) into a decimal fraction, we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction can be converted to an improper fraction using the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]
In our case, the whole number is 15, the numerator is 17, and the denominator is 40.

\[ \text{Improper Fraction} = \left(15 \times 40 + 17\right) / 40 \]

### Step 2: Calculate the numerator
First, we calculate \( 15 \times 40 \):
\[ 15 \times 40 = 600 \]
Now, add 17 to this result:
\[ 600 + 17 = 617 \]
Thus, the improper fraction is:
\[ \frac{617}{40} \]

### Step 3: Divide the numerator by the denominator
Now, we need to divide 617 by 40 to convert it into a decimal:
\[ 617 \div 40 \]

### Step 4: Perform the division
1. **How many times does 40 go into 617?**
- 40 goes into 617 a total of 15 times because \( 40 \times 15 = 600 \).
- Write down 15 and subtract \( 600 \) from \( 617 \):
\[ 617 - 600 = 17 \]

2. **Bring down a decimal point and a zero** (making it 170):
- Now, we have \( 170 \) to divide by \( 40 \).

3. **How many times does 40 go into 170?**
- 40 goes into 170 a total of 4 times because \( 40 \times 4 = 160 \).
- Write down 4 and subtract \( 160 \) from \( 170 \):
\[ 170 - 160 = 10 \]

4. **Bring down another zero** (making it 100):
- Now, we have \( 100 \) to divide by \( 40 \).

5. **How many times does 40 go into 100?**
- 40 goes into 100 a total of 2 times because \( 40 \times 2 = 80 \).
- Write down 2 and subtract \( 80 \) from \( 100 \):
\[ 100 - 80 = 20 \]

6. **Bring down another zero** (making it 200):
- Now, we have \( 200 \) to divide by \( 40 \).

7. **How many times does 40 go into 200?**
- 40 goes into 200 a total of 5 times because \( 40 \times 5 = 200 \).
- Write down 5 and subtract \( 200 \) from \( 200 \):
\[ 200 - 200 = 0 \]

### Final Result
Putting it all together, we find:
\[ 617 \div 40 = 15.425 \]
Thus, the decimal fraction of \( 15 \frac{17}{40} \) is \( 15.425 \).