Fraction Calculator Comparing Fractions

Compare Fractions Using:

\[ \frac{a}{b} \quad \text{vs} \quad \frac{c}{d} \] \[ \text{Method 1: Cross Multiply} \Rightarrow a \times d \quad \text{vs} \quad b \times c \] \[ \text{Method 2: LCM} \Rightarrow \frac{a \times \text{LCM}/b}{\text{LCM}} \quad \text{vs} \quad \frac{c \times \text{LCM}/d}{\text{LCM}} \]

Comparison Result:

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1. What is Fraction Comparison?

Fraction comparison is the process of determining which of two fractions is larger, or if they are equal. This calculator compares fractions using two different methods: cross multiplication and finding a common denominator via LCM (Least Common Multiple).

2. How Does the Calculator Work?

The calculator uses two mathematical approaches:

\[ \text{Cross Multiply:} \quad \frac{a}{b} \quad \text{vs} \quad \frac{c}{d} \Rightarrow a \times d \quad \text{vs} \quad b \times c \] \[ \text{LCM Method:} \quad \frac{a \times \text{LCM}/b}{\text{LCM}} \quad \text{vs} \quad \frac{c \times \text{LCM}/d}{\text{LCM}} \]

3. Methods of Comparison

Cross Multiplication: Multiply numerator of first fraction with denominator of second, and vice versa. Compare these products.

LCM Method: Find the least common denominator, convert both fractions to equivalent fractions with this denominator, then compare numerators.

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions. All denominators must be positive integers. The calculator will show both comparison methods.

5. Frequently Asked Questions (FAQ)

Q1: Which method is better?
A: Both give the same result. Cross multiplication is simpler for one-time comparisons, while LCM method is useful when you need equivalent fractions.

Q2: What if denominators are equal?
A: Simply compare numerators directly - no calculation needed.

Q3: Can I compare improper fractions?
A: Yes, the calculator works for both proper and improper fractions.

Q4: How does it handle negative fractions?
A: Negative values can be entered, but comparison follows standard mathematical rules (e.g., -1/2 > -3/4).

Q5: What about mixed numbers?
A: Convert mixed numbers to improper fractions first before using this calculator.