Comparing Fractions Calculator 3 Fractions

Compare three fractions by cross-multiplication or decimal conversion:

\[ \frac{a}{b} \quad \frac{c}{d} \quad \frac{e}{f} \]

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Comparison Method:

Comparison Result:

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1. What is Fraction Comparison?

Fraction comparison is the process of determining the relative size of two or more fractions. This calculator compares three fractions (a/b, c/d, e/f) using either cross-multiplication or decimal conversion methods.

2. How Does the Calculator Work?

The calculator provides two methods to compare fractions:

Cross Multiplication: \[ a \times d \times f \quad vs \quad c \times b \times f \quad vs \quad e \times b \times d \] Decimal Conversion: \[ \frac{a}{b} \quad vs \quad \frac{c}{d} \quad vs \quad \frac{e}{f} \]

Both methods will correctly determine the order of the fractions from smallest to largest.

3. Comparison Methods Explained

Cross Multiplication: Multiplies numerator of each fraction by denominators of the other fractions. The products are proportional to the original fractions but have common denominators, making comparison straightforward.

Decimal Conversion: Converts each fraction to its decimal equivalent by dividing numerator by denominator. Decimal values can be directly compared.

4. Using the Calculator

Tips: Enter numerators and denominators for all three fractions. Denominators must be positive integers. Choose your preferred comparison method (cross multiplication is exact while decimal conversion may have rounding for repeating decimals).

5. Frequently Asked Questions (FAQ)

Q1: Which method is more accurate?
A: Cross multiplication is mathematically exact. Decimal conversion may have rounding errors for repeating decimals.

Q2: Can I compare improper fractions?
A: Yes, the calculator works with both proper and improper fractions.

Q3: What if two fractions are equal?
A: The calculator will identify equal fractions in the results.

Q4: Can I compare more than three fractions?
A: This calculator is designed for three fractions. For more fractions, you would need to perform multiple comparisons.

Q5: What about negative fractions?
A: The calculator currently handles positive fractions only. For negative fractions, you would need to consider the sign separately.