A graphic designer charges Rs 27 `3/5` for each diagram. Find the amount he will charge if he designs 186 diagrams for a book.

Answer

To solve the problem step by step, we will first convert the mixed fraction into an improper fraction, then calculate the total charge for designing 186 diagrams.

### Step 1: Convert the mixed fraction to an improper fraction
The graphic designer charges Rs 27 `3/5` for each diagram. We need to convert this mixed number into an improper fraction.

- The whole number part is 27.
- The fractional part is `3/5`.

To convert it:
1. Multiply the whole number by the denominator: \(27 \times 5 = 135\).
2. Add the numerator: \(135 + 3 = 138\).
3. Place this result over the original denominator: \(\frac{138}{5}\).

**Improper fraction for the charge per diagram:**
\[ \frac{138}{5} \]

**Hint for Step 1:** Remember that to convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.

### Step 2: Calculate the total charge for 186 diagrams
Now, we need to find the total amount charged for 186 diagrams. We can do this by multiplying the charge for one diagram by the number of diagrams.

\[ \text{Total Charge} = \text{Charge per diagram} \times \text{Number of diagrams} \]
\[ \text{Total Charge} = \frac{138}{5} \times 186 \]

### Step 3: Multiply the fractions
To multiply the fraction by the whole number, we can express 186 as a fraction:

\[ 186 = \frac{186}{1} \]

Now we multiply:
\[ \frac{138}{5} \times \frac{186}{1} = \frac{138 \times 186}{5 \times 1} = \frac{138 \times 186}{5} \]

### Step 4: Calculate \(138 \times 186\)
Now we need to calculate \(138 \times 186\):

\[ 138 \times 186 = 25668 \]

So we have:
\[ \frac{25668}{5} \]

### Step 5: Divide \(25668\) by \(5\)
Now we divide \(25668\) by \(5\):

1. \(5\) goes into \(25\) five times (5 x 5 = 25).
2. Subtract \(25\) from \(25\) to get \(0\), bring down the next digit \(6\).
3. \(5\) goes into \(6\) once (5 x 1 = 5).
4. Subtract \(5\) from \(6\) to get \(1\), bring down the next digit \(6\).
5. \(5\) goes into \(16\) three times (5 x 3 = 15).
6. Subtract \(15\) from \(16\) to get \(1\), bring down the next digit \(8\).
7. \(5\) goes into \(18\) three times (5 x 3 = 15).
8. Subtract \(15\) from \(18\) to get \(3\).

So we have:
\[ \frac{25668}{5} = 5133 \text{ remainder } 3 \]

This can be expressed as:
\[ 5133 \frac{3}{5} \]

### Final Answer
The total amount the graphic designer will charge for designing 186 diagrams is Rs 5133 `3/5`.

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