Simplifying Complex Fractions Calculator
Enter a fraction divided by a fraction and get the simplified result with full step-by-step solution.
Enter the top fraction (numerator fraction) and the bottom fraction (denominator fraction):
| Step | Result |
|---|
| Complex Fraction | Simplified | Decimal |
|---|---|---|
| (1/2) ÷ (1/4) | 2 | 2.0 |
| (2/3) ÷ (4/9) | 3/2 | 1.5 |
| (3/4) ÷ (9/16) | 4/3 | 1.333… |
| (5/6) ÷ (10/3) | 1/4 | 0.25 |
| (7/8) ÷ (7/4) | 1/2 | 0.5 |
| (2/5) ÷ (4/15) | 3/2 | 1.5 |
What Is a Complex Fraction?
A complex fraction is a fraction where the numerator, the denominator, or both contain fractions. Complex fractions are sometimes called compound fractions. Examples include (1/2) divided by (3/4), or a fraction whose numerator itself is (a/b).
Complex fractions appear frequently in algebra, physics, and everyday math such as rate problems, unit conversions, and proportions.
Method 1: Keep Change Flip
The most common method for simplifying a complex fraction is keep change flip, also called multiply by the reciprocal:
- Keep the numerator fraction exactly as it is
- Change the division sign to a multiplication sign
- Flip the denominator fraction to get its reciprocal
- Multiply the two fractions together
- Simplify the result by dividing by the GCD
Method 2: Multiply by LCD
An alternative approach is to find the least common denominator of all fractions in the expression and multiply both the numerator and denominator of the complex fraction by the LCD. This eliminates all inner fractions in one step, leaving a simple fraction to reduce.
How to Reduce a Fraction to Lowest Terms
After simplifying a complex fraction, the result should be reduced to its lowest terms. To do this, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. A fraction is fully reduced when no integer other than 1 divides both parts evenly.
Complex Fractions in Real Life
Complex fractions appear in many practical situations:
- Speed problems: distance divided by time, where both are fractions
- Unit rates: comparing quantities that each involve fractions
- Recipes: scaling ingredient fractions by a fractional serving size
- Algebra: simplifying rational expressions and equations
Frequently Asked Questions
A complex fraction is a fraction in which the numerator, the denominator, or both contain fractions themselves. For example, (1/2) divided by (3/4) is a complex fraction.
To simplify a complex fraction, rewrite the division as multiplication by flipping the denominator fraction (its reciprocal), then multiply numerators together and denominators together. Finally, reduce the resulting fraction to lowest terms by dividing by the GCD.
The keep change flip method means: keep the numerator fraction as it is, change the division operation to multiplication, then flip (take the reciprocal of) the denominator fraction. Then multiply across and simplify.
To reduce a fraction to lowest terms, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. The fraction is in lowest terms when the GCD equals 1.
The LCD method involves finding the least common denominator of all fractions in the complex fraction, then multiplying the entire expression by that LCD to eliminate all inner fractions at once, leaving a simple fraction to reduce.