Comparing 3 Fractions Calculator

Compare three fractions by finding their least common denominator:

\[ \text{Compare } \frac{a}{b}, \frac{c}{d}, \frac{e}{f} \text{ by converting to equivalent fractions with LCD} \]

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 Results:

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1. What is Fraction Comparison?

Comparing fractions involves determining which fraction is larger, smaller, or if they're equal. The most reliable method is to convert them to equivalent fractions with a common denominator (LCD) and then compare the numerators.

2. How Does the Calculator Work?

The calculator uses the following steps:

\[ \text{LCD} = \text{LCM}(b, d, f) \] \[ \frac{a}{b} = \frac{a \times (\text{LCD}/b)}{\text{LCD}} \] \[ \frac{c}{d} = \frac{c \times (\text{LCD}/d)}{\text{LCD}} \] \[ \frac{e}{f} = \frac{e \times (\text{LCD}/f)}{\text{LCD}} \]

Where:

LCM - Least Common Multiple
LCD - Least Common Denominator
a/b, c/d, e/f - The fractions to compare

Explanation: The calculator finds the LCD of all denominators, converts each fraction to an equivalent fraction with this denominator, then compares the numerators.

3. Importance of LCD in Comparison

Details: Using the LCD ensures accurate comparison without changing the value of the fractions. This method works for any set of fractions, regardless of their denominators.

4. Using the Calculator

Tips: Enter the numerators and denominators for all three fractions. All denominators must be positive integers. The calculator will show the equivalent fractions with LCD and their order from smallest to largest.

5. Frequently Asked Questions (FAQ)

Q1: Why can't I just compare the numerators directly?
A: Fractions with different denominators represent different sized portions. You must first make the denominators equal to compare them fairly.

Q2: What if two fractions have the same value?
A: The calculator will list them consecutively in the results. Equivalent fractions will have the same numerator when converted to LCD form.

Q3: Can I compare more than three fractions?
A: This calculator is designed for three fractions, but the same method works for any number of fractions.

Q4: What about negative fractions?
A: Negative fractions can be compared the same way - the LCD method works regardless of sign.

Q5: Is this method better than converting to decimals?
A: Both methods work, but the LCD method maintains exact fractional values without rounding errors that can occur with decimal conversion.