Convert the following fractions into percentages :
`1(5)/(8)`

Answer

To convert the mixed fraction \(1 \frac{5}{8}\) into a percentage, follow these steps:

### Step 1: Convert the mixed fraction into an improper fraction.
A mixed fraction consists of a whole number and a proper fraction. To convert \(1 \frac{5}{8}\) into an improper fraction, we can use the formula:

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

For \(1 \frac{5}{8}\):
- Whole Number = 1
- Numerator = 5
- Denominator = 8

So, we calculate:

\[ 1 \frac{5}{8} = \frac{(1 \times 8) + 5}{8} = \frac{8 + 5}{8} = \frac{13}{8} \]

### Step 2: Convert the improper fraction into a percentage.
To convert a fraction into a percentage, we multiply it by 100.

\[ \text{Percentage} = \left(\frac{13}{8}\right) \times 100 \]

### Step 3: Perform the multiplication.
Now we perform the multiplication:

\[ \frac{13 \times 100}{8} = \frac{1300}{8} \]

### Step 4: Simplify the fraction.
Now, we divide 1300 by 8:

\[ 1300 \div 8 = 162.5 \]

### Step 5: Write the final answer.
Thus, the percentage equivalent of the mixed fraction \(1 \frac{5}{8}\) is:

\[ 162.5\% \]

### Summary of Steps:
1. Convert mixed fraction to improper fraction: \(1 \frac{5}{8} = \frac{13}{8}\)
2. Multiply by 100 to convert to percentage: \(\frac{13}{8} \times 100 = 162.5\%\)

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