https://file.aiquickdraw.com/mathbot/file/1730640783937eb6qvnfd.jpg

To solve for the width of the rectangle in centimeters, we can use the area formula for a rectangle, which states:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Here’s the information we have from the image:
- **Area** = \(1 \frac{7}{8} \, \text{cm}^2\)
- **Length** = \(8 \frac{1}{3} \, \text{cm}\)
- We are asked to find the **Width**, \(w\), and provide it as a fraction in simplest form.

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \(1 \frac{7}{8}\) to an improper fraction:
   \[
   1 \frac{7}{8} = \frac{15}{8}
   \]

2. Convert \(8 \frac{1}{3}\) to an improper fraction:
   \[
   8 \frac{1}{3} = \frac{25}{3}
   \]

### Step 2: Set Up the Equation
Since \(\text{Area} = \text{Length} \times \text{Width}\), we can write:
\[
\frac{15}{8} = \frac{25}{3} \times w
\]

### Step 3: Solve for \(w\)
To isolate \(w\), divide both sides by \(\frac{25}{3}\), which is equivalent to multiplying by the reciprocal \(\frac{3}{25}\):
\[
w = \frac{15}{8} \times \frac{3}{25}
\]

### Step 4: Multiply the Fractions
\[
w = \frac{15 \times 3}{8 \times 25} = \frac{45}{200}
\]

### Step 5: Simplify the Fraction
To simplify \(\frac{45}{200}\), find the greatest common divisor (GCD) of 45 and 200, which is 5:
\[
\frac{45}{200} = \frac{9}{40}
\]

### Final Answer
The width of the rectangle is:
\[
w = \frac{9}{40} \, \text{cm}
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How would the width change if the area were doubled?
2. How do you calculate the area of a triangle with given base and height?
3. If both the length and width were expressed as decimals, how would that affect calculations?
4. How do you simplify a fraction to its simplest form in general?
5. What methods can you use to convert between mixed numbers and improper fractions?

**Tip:** When working with areas, always ensure that units are consistent across all measurements.

What is the width, in centimetres (cm), of this rectangle? Give your answer as a fraction in its simplest form.

Learn how to find the width of a rectangle when the area and length are given. This problem demonstrates converting mixed numbers to improper fractions, setting up algebraic equations, and simplifying fractions. Suitable for Grades 6-8.

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