Convert each of the following fractions into a decimal :
`4(3)/8`

Answer

To convert the mixed fraction \( 4\frac{3}{8} \) into a decimal, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction consists of a whole number and a proper fraction. To convert it to an improper fraction, we use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \div \text{Denominator} \]

For \( 4\frac{3}{8} \):
- Whole number = 4
- Numerator = 3
- Denominator = 8

Calculating the improper fraction:

\[ 4\frac{3}{8} = \frac{(4 \times 8) + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8} \]

### Step 2: Perform long division to convert the improper fraction to a decimal
Now we need to divide 35 by 8 using long division.

1. **Divide 35 by 8**:
- 8 goes into 35 four times (since \( 8 \times 4 = 32 \)).
- Write down 4 and subtract \( 32 \) from \( 35 \):
\[ 35 - 32 = 3 \]

2. **Add a decimal point and a zero**:
- Since 3 is less than 8, we add a decimal point and a zero to make it 30.
- Now, we divide 30 by 8:
- 8 goes into 30 three times (since \( 8 \times 3 = 24 \)).
- Write down 3 and subtract \( 24 \) from \( 30 \):
\[ 30 - 24 = 6 \]

3. **Add another zero**:
- Add another zero to make it 60.
- Now, divide 60 by 8:
- 8 goes into 60 seven times (since \( 8 \times 7 = 56 \)).
- Write down 7 and subtract \( 56 \) from \( 60 \):
\[ 60 - 56 = 4 \]

4. **Add another zero**:
- Add another zero to make it 40.
- Now, divide 40 by 8:
- 8 goes into 40 five times (since \( 8 \times 5 = 40 \)).
- Write down 5 and subtract \( 40 \) from \( 40 \):
\[ 40 - 40 = 0 \]

### Final Result
Putting it all together, we have:

\[ 4\frac{3}{8} = 4.375 \]

### Summary
The decimal equivalent of the mixed fraction \( 4\frac{3}{8} \) is \( 4.375 \).

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