Preeti selects a dress material costing Rs. `35(1)/(2)` per metre. She needs 5 m of the material. How much does she have to pay?

Answer

To find out how much Preeti has to pay for the dress material, we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction.
The cost of the material is given as Rs. \(35 \frac{1}{2}\) per meter. To convert this mixed fraction into an improper fraction, we use the formula:

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

Here, the whole number is 35, the numerator is 1, and the denominator is 2.

\[ \text{Improper Fraction} = \left(35 \times 2 + 1\right) / 2 = \left(70 + 1\right) / 2 = \frac{71}{2} \]

### Step 2: Calculate the total cost for 5 meters.
Now that we have the cost per meter as \(\frac{71}{2}\), we need to find the total cost for 5 meters. We do this by multiplying the cost per meter by the number of meters needed:

\[ \text{Total Cost} = \text{Cost per meter} \times \text{Number of meters} = \frac{71}{2} \times 5 \]

To perform the multiplication:

\[ \text{Total Cost} = \frac{71 \times 5}{2} = \frac{355}{2} \]

### Step 3: Convert the improper fraction back to a mixed fraction.
Now we need to convert \(\frac{355}{2}\) back into a mixed fraction. We do this by dividing the numerator by the denominator:

\[ 355 \div 2 = 177 \quad \text{(Quotient)} \]
\[ 355 - (177 \times 2) = 1 \quad \text{(Remainder)} \]

Thus, we can express \(\frac{355}{2}\) as:

\[ 177 \frac{1}{2} \]

### Final Answer:
Preeti has to pay Rs. \(177 \frac{1}{2}\).

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