Comparing Fractions Calculator

How to Compare Fractions

Comparing fractions might seem challenging at first — it's a bit like comparing apples and oranges when the denominators are different. Fortunately, there are several reliable methods to determine which fraction is larger. Our calculator above uses all of them and shows the complete step-by-step work.

Below you'll find four methods explained in detail, each with a worked example using the same pair of fractions: 2/7 and 3/5.

Method One: Compare Fractions by Converting to Decimals

The simplest method is to convert each fraction to a decimal by dividing the numerator by the denominator. Once both fractions are in decimal form, you can compare them directly — the larger decimal is the larger fraction.

Example: Compare 2/7 and 3/5.

• 2/7 = 2 ÷ 7 = 0.2857…
• 3/5 = 3 ÷ 5 = 0.6000

Since 0.6 > 0.2857, we know that 3/5 > 2/7.

Use our Long Division Calculator to see the full division steps when converting fractions to decimals.

Method Two: Compare by Finding the Common Denominator

Rewrite both fractions as equivalent fractions with the same denominator. Then simply compare the numerators — the fraction with the larger numerator is the larger fraction.

Example: Compare 2/7 and 3/5.

• Find the LCD (Least Common Denominator): LCM(7, 5) = 35
• 2/7 = (2 × 5) / (7 × 5) = 10/35
• 3/5 = (3 × 7) / (5 × 7) = 21/35

Compare numerators: 21 > 10, so 3/5 > 2/7.

Method Three: Compare Fractions with the Same Numerator

When two fractions have the same numerator, there's a shortcut: the fraction with the smaller denominator is larger.

Why? Because a smaller denominator means the whole is divided into fewer pieces, so each piece is bigger.

Example: Compare 3/5 and 3/8.

• Both numerators are 3.
• 5 < 8, so fifths are larger than eighths.
• Therefore, 3/5 > 3/8.

Method Four: Cross Multiplication

Cross multiplication is a quick, reliable method that always works. Multiply each numerator by the opposite denominator and compare the products.

Formula: To compare a/b and c/d, compute a × d and c × b.

• If a × d > c × b, then a/b > c/d
• If a × d < c × b, then a/b < c/d
• If a × d = c × b, then a/b = c/d

Example: Compare 2/7 and 3/5.

• 2 × 5 = 10
• 3 × 7 = 21
• 10 < 21, so 2/7 < 3/5.

How to Compare Fractions to Decimals and Percentages

To compare a fraction to a decimal or percentage, convert all values to the same format:

• Fraction → Decimal: Divide the numerator by the denominator. Example: 3/8 = 0.375
• Fraction → Percentage: Convert to decimal, then multiply by 100. Example: 3/8 = 0.375 = 37.5%
• Percentage → Decimal: Divide by 100. Example: 45% = 0.45

Once all values are in the same format, compare them directly. Use our Percentage Calculator for quick conversions.

Frequently Asked Questions

Why do we compare fractions?

Comparing fractions is essential for:

• Determining which quantity is larger or smaller (e.g., is 3/4 cup more than 2/3 cup?)
• Ordering and ranking data represented as fractions
• Deciding between options in recipes, measurements, and science experiments
• Evaluating performance metrics (e.g., batting averages, completion rates)

Why is it easier to compare decimals instead of fractions?

Decimals use the base-10 number system, which makes their relative size immediately visible. Comparing 0.75 and 0.6 is trivial — you can see at a glance that 0.75 is larger. With fractions like 3/4 and 3/5, the comparison requires extra steps because the denominators are different.

How do you compare fractions with whole numbers?

Convert the whole number to a fraction by putting it over 1 (e.g., 3 = 3/1), then use any of the four methods above. Alternatively, convert the fraction to a decimal and compare directly. For example: Is 2/3 greater than 1? Since 2/3 = 0.667 and 1 = 1.000, we know 2/3 < 1.

How do you compare more than two fractions at a time?

The best approach is to find a common denominator for all the fractions using the LCM of all denominators. Convert each fraction to an equivalent fraction with that denominator, then rank the numerators from smallest to largest. Alternatively, convert all fractions to decimals and sort them.