Quickly compare two fractions and see exactly which one is greater, smaller, or if they are equal. This calculator uses cross multiplication and simplification to clearly show the reasoning behind the comparison.
Enter two fractions to get an instant result with step-by-step explanation.
How to Use the Comparing Fractions Calculator
Using the calculator is simple:
- Enter the numerator and denominator for the first fraction
- Enter the numerator and denominator for the second fraction
- Click Compare
- View the result and explanation instantly
The output will show:
- Simplified fractions
- Cross multiplication steps
- A clear comparison result
- Optional decimal values for verification
What Does It Mean to Compare Fractions?
Comparing fractions means determining which fraction is:
- Greater than (>)
- Less than (<)
- Equal to (=)
This helps you understand the relative size of fractions.
How the Calculator Works
The calculator uses a reliable method called cross multiplication.
For two fractions:
a / b and c / d
Compare:
If equal → fractions are equal
a × d
c × b
If a × d > c × b → first fraction is larger
If a × d < c × b → second fraction is larger
Why Simplifying First Helps
Before comparing, fractions are often simplified to their lowest terms.
Example:
- 35/45 → 7/9
- 55/60 → 11/12
This makes the comparison clearer and easier to understand.
Example Explained
Let’s compare:
35/45 and 55/60
Step 1: Simplify
→ 35/45 = 7/9
→ 55/60 = 11/12
Step 2: Cross multiply
→ 7 × 12 = 84
→ 11 × 9 = 99
Step 3: Compare
→ 84 < 99
So:
7/9 < 11/12
Frequently Asked Questions
Q1: How do you compare fractions with different denominators?
Use cross multiplication or convert them to a common denominator.
Q2: Why does cross multiplication work?
It compares equivalent values without needing to convert fractions directly.
Q3: Should I simplify fractions first?
It helps make the process clearer, but it is not always required.
Q4: Can fractions be equal?
Yes, different fractions can represent the same value, such as 1/2 and 2/4.
Q5: Is converting to decimals always accurate?
Yes, but recurring decimals may be rounded.