On a certain map, `(3)/(8)` of an inch represents 120 miles. How many miles does `1(3)/(4)` inches represent?

Options

A. `300`
B. `360`
C. `480`
D. `560`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between inches on the map and miles.
We know that \( \frac{3}{8} \) inches on the map represents 120 miles.

### Step 2: Find out how many miles 1 inch represents.
To find out how many miles 1 inch represents, we can use the unitary method.

\[ 1 \text{ inch} = \frac{120 \text{ miles}}{\frac{3}{8}} = 120 \times \frac{8}{3} \]

### Step 3: Calculate the value of 1 inch in miles.
Now, we perform the multiplication:

\[ 1 \text{ inch} = 120 \times \frac{8}{3} = \frac{960}{3} = 320 \text{ miles} \]

### Step 4: Convert the mixed fraction \( 1 \frac{3}{4} \) into an improper fraction.
The mixed fraction \( 1 \frac{3}{4} \) can be converted as follows:

\[ 1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \]

### Step 5: Find out how many miles \( \frac{7}{4} \) inches represent.
Now that we know 1 inch represents 320 miles, we can find out how many miles \( \frac{7}{4} \) inches represent:

\[ \frac{7}{4} \text{ inches} = \frac{7}{4} \times 320 \text{ miles} \]

### Step 6: Calculate the total miles represented by \( \frac{7}{4} \) inches.
Now we perform the multiplication:

\[ \frac{7}{4} \times 320 = \frac{7 \times 320}{4} = \frac{2240}{4} = 560 \text{ miles} \]

### Conclusion
Thus, \( 1 \frac{3}{4} \) inches on the map represents **560 miles**.

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