Complex Fractions Worksheet
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Complex Fractions Worksheet
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Worked Example
Problem: (3/4) / (9/16)
- Rewrite as a division problem.— (3/4) / (9/16) means (3/4) ÷ (9/16).
- Apply Keep-Change-Flip.— Keep 3/4, change ÷ to ×, flip 9/16 to get 16/9. Expression is now 3/4 × 16/9.
- Cross-cancel common factors.— 3 and 9 share factor 3 (3→1, 9→3). 16 and 4 share factor 4 (16→4, 4→1). Becomes 1/1 × 4/3.
- Multiply and simplify.— 1 × 4 = 4 and 1 × 3 = 3, giving 4/3 = 1 1/3.
Answer: 1 1/3
Frequently Asked Questions
A complex fraction has a fraction in its numerator, its denominator, or both. The goal is always to simplify it into a single ordinary fraction.
Method 1: Rewrite as a division problem (top ÷ bottom) and apply Keep-Change-Flip. Method 2: Multiply numerator and denominator by the LCD of all inner fractions.
They appear frequently in algebra when simplifying rational expressions, and in real-world rate problems like miles per hour divided by hours per trip.