The price of one orange is Rs. `13 (1)/(4)`. Divya buys oranges for Rs. `185 (1)/(2)`. How many oranges did she buy?

Answer

To solve the problem of how many oranges Divya bought, we will follow these steps:

### Step 1: Convert the mixed fraction of the price of one orange into an improper fraction.
The price of one orange is given as Rs. \( 13 \frac{1}{4} \).

To convert this into an improper fraction:
\[ 13 \frac{1}{4} = \frac{(13 \times 4) + 1}{4} = \frac{52 + 1}{4} = \frac{53}{4} \]

### Step 2: Convert the total amount Divya spent into an improper fraction.
The total amount spent is given as Rs. \( 185 \frac{1}{2} \).

To convert this into an improper fraction:
\[ 185 \frac{1}{2} = \frac{(185 \times 2) + 1}{2} = \frac{370 + 1}{2} = \frac{371}{2} \]

### Step 3: Set up the division to find the number of oranges.
To find out how many oranges Divya bought, we need to divide the total amount spent by the price of one orange:
\[ \text{Number of oranges} = \frac{371/2}{53/4} \]

### Step 4: Perform the division of fractions.
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{371}{2} \div \frac{53}{4} = \frac{371}{2} \times \frac{4}{53} \]

### Step 5: Simplify the expression.
Now we can simplify:
\[ = \frac{371 \times 4}{2 \times 53} \]
First, simplify \( \frac{4}{2} = 2 \):
\[ = \frac{371 \times 2}{53} \]

### Step 6: Calculate the multiplication.
Now, we calculate \( 371 \times 2 \):
\[ = \frac{742}{53} \]

### Step 7: Perform the division.
Now, we divide \( 742 \) by \( 53 \):
\[ 742 \div 53 = 14 \]

Thus, Divya bought **14 oranges**.

### Summary of Steps:
1. Convert mixed fraction \( 13 \frac{1}{4} \) to improper fraction \( \frac{53}{4} \).
2. Convert mixed fraction \( 185 \frac{1}{2} \) to improper fraction \( \frac{371}{2} \).
3. Set up the division \( \frac{371/2}{53/4} \).
4. Multiply by the reciprocal \( \frac{371}{2} \times \frac{4}{53} \).
5. Simplify the expression.
6. Calculate \( 371 \times 2 \).
7. Divide \( 742 \) by \( 53 \) to get the final answer.