A rectangular tabletop has an area of \(\displaystyle \frac{9}{8}\) square yards. Its length is \(\displaystyle \frac{3}{2}\) yards. Find the width.
Step 1: Divide the area by the known length.
\(\displaystyle w=\frac{9}{8}\div\frac{3}{2}\)
Step 2: Multiply by the reciprocal.
\(\displaystyle w=\frac{9}{8}\times\frac{2}{3}\)
Step 3: Multiply and simplify.
\(\displaystyle w=\frac{18}{24}=\frac{3}{4}\)
Final Answer:
\(\displaystyle \boxed{w=\frac{3}{4}\text{ yd}}\)
Example 3 – Find the Missing Side Length
A rectangle has an area of \(\displaystyle \frac{35}{24}\) square feet. One side measures \(\displaystyle \frac{7}{4}\) feet. Find the missing dimension.
Equation: A mathematical statement showing two expressions are equal.
Reciprocal: A fraction flipped upside down.
Improper Fraction: A fraction with a numerator greater than or equal to the denominator.
💡 Main Idea
When you know the area of a rectangle and one dimension, you can find the missing dimension by dividing the area by the known side. These problems connect geometry, fraction division, and equation writing in a very natural way.
📚 What You Should Already Know
Before solving these problems, you should know how to use the area formula for rectangles, how to divide fractions by multiplying by the reciprocal, and how to simplify fractions.
🚀 What Comes Next
Next, students can apply this same reasoning to more challenging word problems involving mixed numbers, equations with variables, and geometric situations where a missing side length must be determined.
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