Example 3 – How Many Fourths Are in One and One-Half?
Divide:
\(\displaystyle 1\frac{1}{2}\div\frac{1}{4}\)
Step 1: Rewrite the mixed number as fourths.
\(\displaystyle 1\frac{1}{2}=\frac{6}{4}\)
Step 2: Interpret the division question.
How many one-fourth-size pieces fit inside six-fourths?
Step 3: Use the fraction strips. The model contains six shaded fourths.
4 fourths + 2 fourths = 6 fourths
Therefore, six groups of one-fourth fit inside one and one-half.
Step 4: Verify by multiplying by the reciprocal.
\(\displaystyle \frac{6}{4}\times\frac{4}{1}=6\)
Final Answer:
\(\boxed{6}\)
💡 Main Idea
This lesson focuses on solving fraction division word problems by interpreting division as counting equal-size groups. Visual models help students see how many small pieces fit into a larger quantity before applying the standard fraction division algorithm.
🚀 What Comes Next
Students will continue solving fraction division problems involving mixed numbers, measurement situations, and real-world applications such as rates and unit conversions.
