Comparing Fractions Calculator

How the Comparing Fractions Calculator Works

To compare fractions accurately, both fractions must be expressed with a common denominator — the same bottom number. Once denominators match, the fraction with the larger numerator is greater.

Formula for comparing fractions:

If
a/b and c/d are two fractions,
then compare by finding their equivalent values with the Lowest Common Denominator (LCD):

a/b = (a × d) / (b × d)
c/d = (c × b) / (d × b)

Now, compare the numerators directly.

For example, to compare 5/6 and 3/8:

1. Find the LCD of 6 and 8 → LCD = 24
2. Convert both fractions:
   5/6 = 20/24
   3/8 = 9/24
3. Compare numerators: 20 > 9, therefore 5/6 > 3/8

This same logic applies to improper fractions and mixed numbers — just convert them to improper fractions first before comparing.

Comparing Fractions with Unlike Denominators

When denominators differ, you can’t compare directly. Instead:

1. Find the Lowest Common Denominator (LCD).
2. Convert each fraction to have that denominator.
3. Compare the numerators.

For example:
Compare 7/9 and 5/6
LCD of 9 and 6 is 18.
7/9 = 14/18
5/6 = 15/18
Since 15 > 14, 5/6 is greater than 7/9.

If you’re struggling to find the LCD, try the LCD Calculator — it saves time and ensures accuracy.

Comparing Mixed Numbers and Improper Fractions

Mixed numbers like 2 ⅓ can be tricky to compare directly. Convert them to improper fractions first.

Example:
2 ⅓ = (2 × 3 + 1)/3 = 7/3
Now compare 7/3 with another fraction, say 8/5.
Find LCD of 3 and 5 → LCD = 15
7/3 = 35/15
8/5 = 24/15
Since 35 > 24, 7/3 (or 2 ⅓) is larger.

You can use our Fraction to Decimal Calculator to cross-check your result in decimal form. It converts any fraction to a decimal, making comparison effortless.

Comparing Decimals and Integers

The Comparing Fractions Calculator also allows comparison between decimals and integers.
Simply convert each value into a consistent form:

• Convert decimals to fractions (e.g., 0.75 = 3/4).
• Convert integers to fractions (e.g., 5 = 5/1).

Then use the same LCD-based comparison method.

For a quick conversion between decimals and fractions, visit the Decimal to Fraction Calculator.

Manual Method vs Online Fraction Comparison

Manually comparing fractions requires converting, finding LCDs, and simplifying — a process prone to errors.
The Comparing Fractions Calculator automates all these steps instantly, displaying which fraction is greater or smaller, and even handles decimals, mixed numbers, or negative fractions.

This makes it perfect for math students checking their homework or anyone verifying calculations involving ratios, recipes, or measurements.

Example Problem

Compare 2/5 and 3/7

1. Find the LCD: 35
2. Convert both fractions:
   2/5 = 14/35
   3/7 = 15/35
3. Compare numerators: 14 < 15 → 2/5 < 3/7

Thus, 3/7 is greater.

Why Understanding Fraction Comparison Matters

Fractions form the foundation of algebra, ratios, and proportions. Comparing them helps build intuition about relative values, scaling, and equivalent expressions. Whether you’re balancing ingredients in a recipe or solving complex equations, mastering this concept ensures mathematical accuracy.

The Comparing Fractions Calculator makes fraction comparison quick, clear, and accurate. By using simple mathematical principles — common denominators, numerator comparison, and fraction-to-decimal conversion — it eliminates confusion and builds confidence in your results.

Try comparing fractions, decimals, or mixed numbers directly with this tool and explore other helpful math calculators to deepen your understanding of fractions and numerical relationships.