Lipika reads a book for `1 frac {3}{4}` hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

Options

A. `10 frac{1}{2}`
B. `10`
C. `20`
D. `11/2`

Explanation

To find out how many hours in total Lipika required to read the book, we can follow these steps:

### Step 1: Identify the daily reading time and total days
Lipika reads for \(1 \frac{3}{4}\) hours every day and she reads for 6 days.

### Step 2: Convert the mixed fraction to an improper fraction
To convert \(1 \frac{3}{4}\) to an improper fraction:
- Multiply the whole number (1) by the denominator (4): \(1 \times 4 = 4\)
- Add the numerator (3): \(4 + 3 = 7\)
- So, \(1 \frac{3}{4} = \frac{7}{4}\)

### Step 3: Multiply the daily reading time by the number of days
Now we need to find the total hours by multiplying the daily reading time by the number of days:
\[ \text{Total hours} = \text{Daily reading time} \times \text{Number of days} = \frac{7}{4} \times 6 \]

### Step 4: Simplify the multiplication
We can simplify the multiplication:
\[ \frac{7}{4} \times 6 = \frac{7 \times 6}{4} = \frac{42}{4} \]

### Step 5: Simplify the fraction
Now simplify \(\frac{42}{4}\):
- Divide both the numerator and the denominator by 2:
\[ \frac{42 \div 2}{4 \div 2} = \frac{21}{2} \]

### Step 6: Convert the improper fraction to a mixed number
To convert \(\frac{21}{2}\) to a mixed number:
- Divide 21 by 2, which gives 10 with a remainder of 1.
- So, \(\frac{21}{2} = 10 \frac{1}{2}\)

### Step 7: Write the final answer
Thus, the total time Lipika took to read the book is \(10 \frac{1}{2}\) hours or 10.5 hours.