Dividing Fractions - Find the Missing Side of a Rectangle

📝 Practice Worksheets

Dividing Fractions Word Problems Dividing Fractions Word Problems 2 Dividing Fractions and Mixed Numbers

🛠️ Related Tools

🔑 Key Concepts

Area of a rectangle is found using \( A = l \times w \).
You can divide the area by a known dimension to find a missing dimension.
Write an equation to represent the relationship.
Convert mixed numbers to improper fractions before dividing.
Always express the final answer in the requested form.

✏️ Worked Examples – Find a Missing Rectangle Dimension Using Fraction Division

Example 1 – Find the Width

A rectangular garden has an area of \(42\frac{3}{4}\) square feet and a length of \(5\frac{1}{2}\) feet. Find the width.

Step 1: Divide the area by the known length.

\(\displaystyle w=42\frac{3}{4}\div5\frac{1}{2}\)

Step 2: Convert the mixed numbers to improper fractions.

\(\displaystyle w=\frac{171}{4}\div\frac{11}{2}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle w=\frac{171}{4}\times\frac{2}{11}\)

Step 4: Multiply and simplify.

\(\displaystyle w=\frac{342}{44}=\frac{171}{22}\)

Step 5: Convert the improper fraction to a mixed number.

\(\displaystyle \frac{171}{22}=7\frac{17}{22}\)

Final Answer:

\(\displaystyle \boxed{w=7\frac{17}{22}\text{ ft}}\)

Example 2 – Find the Length

A rectangular room has an area of \(63\frac{1}{2}\) square feet and a width of \(7\frac{1}{4}\) feet. Find the length.

Step 1: Divide the area by the known width.

\(\displaystyle l=63\frac{1}{2}\div7\frac{1}{4}\)

Step 2: Convert the mixed numbers to improper fractions.

\(\displaystyle l=\frac{127}{2}\div\frac{29}{4}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle l=\frac{127}{2}\times\frac{4}{29}\)

Step 4: Multiply and simplify.

\(\displaystyle l=\frac{508}{58}=\frac{254}{29}\)

Step 5: Convert the improper fraction to a mixed number.

\(\displaystyle \frac{254}{29}=8\frac{22}{29}\)

Final Answer:

\(\displaystyle \boxed{l=8\frac{22}{29}\text{ ft}}\)

Example 3 – Find the Missing Side Length

A rectangular patio has an area of \(48\frac{1}{4}\) square feet. One side measures \(6\frac{1}{2}\) feet. Find the missing dimension.

Step 1: Divide the area by the known side length.

\(\displaystyle d=48\frac{1}{4}\div6\frac{1}{2}\)

Step 2: Convert the mixed numbers to improper fractions.

\(\displaystyle d=\frac{193}{4}\div\frac{13}{2}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle d=\frac{193}{4}\times\frac{2}{13}\)

Step 4: Multiply and simplify.

\(\displaystyle d=\frac{386}{52}=\frac{193}{26}\)

Step 5: Convert the improper fraction to a mixed number.

\(\displaystyle \frac{193}{26}=7\frac{11}{26}\)

Final Answer:

\(\displaystyle \boxed{d=7\frac{11}{26}\text{ ft}}\)

🧠 Math Vocabulary

Area: The amount of space inside a shape.
Dimension: A measurement such as length or width.
Equation: A mathematical statement showing two expressions are equal.
Reciprocal: A fraction flipped upside down.
Improper Fraction: A fraction with a numerator greater than 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. Writing an equation helps organize the information and makes the solution process clear and systematic.

📚 What You Should Already Know

Before solving these problems, you should understand how to find the area of a rectangle, convert mixed numbers to improper fractions, and divide fractions using multiplication by the reciprocal.

🚀 What Comes Next

Next, you will write and solve equations involving unknown values in geometry and real-world situations. You will also apply these skills to multi-step problems involving area, perimeter, and volume.