Dividing Fractions to Solve Word Problems

📝 Practice Worksheets

Dividing Fractions Word Problems - 1 Dividing Fractions Word Problems - 2 Dividing Fractions Word Problems - 3 Dividing Fractions and Mixed Numbers

🛠️ Related Tools

Fraction Operations Practice

🔑 Key Concepts

Word problems often signal division with phrases like how many times, how much bigger, or how many groups.
When comparing one quantity to another multiplicatively, division is often the correct operation.
Write the comparison as the first quantity divided by the second quantity.
Rename mixed numbers as improper fractions before dividing.
Use keep-change-flip to divide fractions and mixed numbers.

✏️ Worked Examples – Recognizing and Solving Fraction Division Word Problems

Example 1 – Compare Two Heights

Kyle’s father is \(6\frac{1}{4}\) feet tall. Kyle is 5 feet tall. How many times as tall is Kyle’s father as Kyle?

Step 1: Identify the operation.

The phrase how many times as tall asks for a multiplicative comparison, so divide the father’s height by Kyle’s height.

\(\displaystyle 6\frac{1}{4}\div5\)

Step 2: Rewrite the mixed number and whole number as fractions.

\(\displaystyle 6\frac{1}{4}=\frac{25}{4}\)

\(\displaystyle 5=\frac{5}{1}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{25}{4}\times\frac{1}{5}\)

Step 4: Simplify and convert to a mixed number.

\(\displaystyle \frac{25}{20}=\frac{5}{4}=1\frac{1}{4}\)

Final Answer:

\(\displaystyle \boxed{1\frac{1}{4}\text{ times as tall}}\)

Example 2 – Compare Two Jump Lengths

Jacquelyn’s first jump was \(14\frac{3}{4}\) feet. Her second jump was \(11\frac{4}{5}\) feet. How many times as long was her first jump as her second jump?

Step 1: Identify the operation.

The phrase how many times as long indicates a multiplicative comparison, so divide the first length by the second length.

\(\displaystyle 14\frac{3}{4}\div11\frac{4}{5}\)

Step 2: Rewrite both mixed numbers as improper fractions.

\(\displaystyle 14\frac{3}{4}=\frac{59}{4}\)

\(\displaystyle 11\frac{4}{5}=\frac{59}{5}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{59}{4}\times\frac{5}{59}\)

Step 4: Simplify the common factor and convert to a mixed number.

\(\displaystyle \frac{5}{4}=1\frac{1}{4}\)

Final Answer:

\(\displaystyle \boxed{1\frac{1}{4}\text{ times as long}}\)

Example 3 – Find the Number of Batches

A recipe uses \(\frac{3}{4}\) cup of sugar for one batch. You have \(2\frac{1}{4}\) cups of sugar. How many batches can you make?

Step 1: Identify the operation.

The question asks how many three-fourths-cup groups fit into the total amount of sugar, so divide.

\(\displaystyle 2\frac{1}{4}\div\frac{3}{4}\)

Step 2: Rewrite the mixed number as an improper fraction.

\(\displaystyle 2\frac{1}{4}=\frac{9}{4}\)

Step 3: Multiply by the reciprocal.

\(\displaystyle \frac{9}{4}\times\frac{4}{3}\)

Step 4: Simplify.

\(\displaystyle \frac{36}{12}=3\)

Final Answer:

\(\boxed{3\text{ batches}}\)

🧠 Math Vocabulary

How many times: a phrase that usually signals division in comparison problems.
How many groups: a clue that one quantity is being divided into equal groups.
Times taller / times longer: comparison language that often means divide one amount by another.
Improper fraction: a fraction with a numerator greater than or equal to the denominator.
Keep-change-flip: keep the first fraction, change division to multiplication, and flip the second fraction.

💡 Main Idea

This lesson helps students recognize when a word problem is asking for division, even when the operation is not stated directly. Context clues like how many times, how many groups, and multiplicative comparisons often signal that one quantity should be divided by another. Once the problem is written correctly, students can solve it using fraction division strategies.

📚 What You Should Already Know

Before watching this video, students should know how to convert mixed numbers to improper fractions, how to divide fractions using keep-change-flip, and how to simplify answers. It also helps if they are already familiar with comparison language in word problems.

🚀 What Comes Next

After solving dividing fractions word problems, students can move into more advanced multi-step applications involving rates, measurement, recipes, scale problems, and algebraic reasoning with rational numbers.

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