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?

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.