∿Mixed Number Lab

Comparison fundamentals

Compare Fractions

Learn how to compare fractions and mixed numbers using four methods: common denominators, cross multiplication, decimal conversion, and whole-number-first. Includes a free instant comparison tool and 12 worked examples.

5 min readGrade 4-7Instant comparator12 examplesMixed numbers4 methods

Written by

Mixed Number Lab Editorial Team

Focus

Which fraction is bigger?

Updated

2026-05-11

Core rule: Convert to the same denominator, then compare numerators

Quick Preview

Find which fraction is greater, smaller, or equal

Left value

3/4

>

Right value

2/3

LCD = 12 -> 9/12 > 8/12

Instant Comparator

Compare two fractions or mixed numbers instantly

Enter two fractions or mixed numbers to see which is greater, with full step-by-step reasoning.

Instant Comparator

Enter two fractions or mixed numbers to compare values with a cross-check and full step-by-step reasoning.

Left value

Enter a whole part and a fraction.

Use +/- or drag a field sideways to adjust quickly.

Right value

Enter a whole part and a fraction.

Use +/- or drag a field sideways to adjust quickly.

In This Guide

Quick Refresher

What does it mean to compare fractions?

Comparing fractions means deciding which of two fractions represents a larger or smaller amount, or whether they are equal. The challenge is that fractions use different denominators, which makes direct comparison impossible without a common reference point.

3/4 and 2/3 look close, but which is bigger? Converting both to twelfths, 9/12 and 8/12, makes the answer obvious.

Smaller

2/3 = 8/12

Fewer twelfths.

Result

2/3 < 3/4

The comparison symbol.

Larger

3/4 = 9/12

More twelfths.

Key idea: Two fractions can only be compared directly when they share the same denominator. The fraction with the larger numerator is the greater value.

Why Compare

When you need to compare fractions

Fraction comparison appears in ordering, simplification checks, recipes, and the classic which is greater test question.

Ordering fractions

Ordering

Sorting a list from least to greatest requires pairwise comparison.

Order fractions

Simplifying first

Prep

Always simplify before comparing to avoid unnecessary large numbers.

Simplify first

Recipe scaling

Real life

Deciding whether 2/3 cup or 3/4 cup is more requires a direct comparison.

See cooking examples

Test problems

Practice

Which is greater? is one of the most common fraction question types.

Use the calculator

Method 1

Convert both fractions to the same denominator, then compare numerators

The common denominator method is the most reliable approach and the one taught in most classrooms. Once both fractions use the same denominator, the numerators tell you everything.

1

Find the LCD of the two denominators

Use the least common denominator so both fractions count the same-sized parts.

textLCD(4,3)=12
2

Convert both fractions to the LCD

Rewrite each fraction as an equivalent fraction with denominator 12.

frac34=frac912,quad frac23=frac812
3

Compare the numerators

Once denominators match, the larger numerator means the larger fraction.

9 > 8
4

Write the result with the original fractions

Return to the original values when writing the final comparison.

frac34 > frac23
Tip: If the denominators are already the same, skip straight to comparing the numerators.

Common Reference

frac34=frac912>frac812=frac23

Example 1

3/4 vs 2/3

Twelfths make the comparison obvious.

  1. 1.LCD = 12.
  2. 2.3/4 = 9/12 and 2/3 = 8/12.
  3. 3.9/12 is greater than 8/12.

Answer: 3/4 > 2/3

Example 2

1/2 vs 3/8

Convert halves to eighths.

  1. 1.LCD = 8.
  2. 2.1/2 = 4/8 and 3/8 stays 3/8.
  3. 3.4/8 is greater than 3/8.

Answer: 1/2 > 3/8

Example 3

5/6 vs 7/9

Both fractions convert cleanly to eighteenths.

  1. 1.LCD = 18.
  2. 2.5/6 = 15/18 and 7/9 = 14/18.
  3. 3.15/18 is greater than 14/18.

Answer: 5/6 > 7/9

Example 4

2/5 vs 4/10

Equivalent fractions land on the same numerator after conversion.

  1. 1.LCD = 10.
  2. 2.2/5 = 4/10 and 4/10 stays 4/10.
  3. 3.4/10 equals 4/10.

Answer: 2/5 = 4/10

Method 2

Cross-multiply to compare without finding the LCD

Cross multiplication gives the same result as the common denominator method but skips the LCD step. Multiply the numerator of each fraction by the denominator of the other, then compare the two products.

1

Multiply the left numerator by the right denominator

This creates the left cross product.

3 times 3 = 9
2

Multiply the right numerator by the left denominator

This creates the right cross product.

2 times 4 = 8
3

Compare the products

The products correspond to the original fractions.

9 > 8 Rightarrow frac34 > frac23
Tip: This method is safest with positive fractions. For negative values, use common denominators or decimals.

Cross Multiplication Rule

a/b vs c/d

Compare: a x d vs b x c

If a x d > b x c, then a/b > c/d.

If a x d < b x c, then a/b < c/d.

If a x d = b x c, then a/b = c/d.

Cross Example 1

3/4 vs 2/3

The left cross product is larger.

  1. 1.Left product: 3 x 3 = 9.
  2. 2.Right product: 2 x 4 = 8.
  3. 3.9 > 8.

Answer: 3/4 > 2/3

Cross Example 2

5/8 vs 3/5

The products differ by one.

  1. 1.Left product: 5 x 5 = 25.
  2. 2.Right product: 3 x 8 = 24.
  3. 3.25 > 24.

Answer: 5/8 > 3/5

Cross Example 3

4/7 vs 8/14

Equal cross products mean equal fractions.

  1. 1.Left product: 4 x 14 = 56.
  2. 2.Right product: 8 x 7 = 56.
  3. 3.56 = 56.

Answer: 4/7 = 8/14

Method 3

Convert both fractions to decimals, then compare

Converting to decimals is the most intuitive method for many students because decimal comparison is straightforward. Divide each numerator by its denominator, then compare the decimal values.

1

Convert each fraction to a decimal

Divide each numerator by its denominator.

frac34=3div4=0.75,quad frac23=2div3=0.overline6
2

Compare the decimal values

Decimal comparison is direct once both values use decimal notation.

0.75 > 0.666ldots
3

Write the result with the original fractions

Use the original fractions in the final answer.

frac34 > frac23
Tip: This method is especially useful for mixed numbers because whole-number parts are easy to see in decimals.

Mixed Number Example

Compare 2 3/4 and 2 2/3. 2 3/4 = 2.75, while 2 2/3 = 2.666... Result: 2 3/4 > 2 2/3.

Decimal Example 1

3/4 vs 2/3

A terminating decimal and a repeating decimal are easy to compare.

  1. 1.3/4 = 0.75.
  2. 2.2/3 = 0.666...
  3. 3.0.75 is greater.

Answer: 3/4 > 2/3

Decimal Example 2

1 1/2 vs 1 3/5

Decimals make mixed-number comparison direct.

  1. 1.1 1/2 = 1.5.
  2. 2.1 3/5 = 1.6.
  3. 3.1.5 is smaller.

Answer: 1 1/2 < 1 3/5

Decimal Example 3

5/4 vs 6/5

Improper fractions compare clearly after division.

  1. 1.5/4 = 1.25.
  2. 2.6/5 = 1.2.
  3. 3.1.25 is greater.

Answer: 5/4 > 6/5

Method 4

Compare mixed numbers by whole part first, fraction part second

When comparing mixed numbers, you can often skip full conversion. If the whole number parts are different, the larger whole number wins immediately. Only compare the fraction parts when the whole numbers are equal.

1

Compare the whole number parts

If the whole numbers are different, the larger whole number wins immediately.

3frac14 > 2frac78quad textbecause 3>2
2

If whole numbers match, compare fraction parts

Use common denominators or cross multiplication on the fraction parts only.

2frac34text vs 2frac23Rightarrow frac34>frac23Rightarrow 2frac34>2frac23

Decision Tree

Are the whole numbers different?

YES -> Larger whole number = larger mixed number.

NO -> Compare fraction parts using Method 1 or 2.

If fractions match, the mixed numbers are equal.

Whole First Example 1

3 1/4 vs 2 7/8

Different whole numbers decide the comparison immediately.

  1. 1.Compare whole parts: 3 > 2.
  2. 2.No fraction comparison is needed.

Answer: 3 1/4 > 2 7/8

Whole First Example 2

2 3/4 vs 2 2/3

Equal whole numbers mean the fraction parts decide.

  1. 1.Compare whole parts: 2 = 2.
  2. 2.Compare fraction parts: 3/4 > 2/3.

Answer: 2 3/4 > 2 2/3

Whole First Example 3

1 5/6 vs 1 5/6

Both the whole and fraction parts match.

  1. 1.Compare whole parts: 1 = 1.
  2. 2.Compare fraction parts: 5/6 = 5/6.

Answer: 1 5/6 = 1 5/6

Compare the four fraction comparison methods

Use common denominators as the default, then choose shortcuts when the numbers make them useful.

CompareMethod 1: Common DenominatorMethod 2: Cross MultiplyMethod 3: DecimalMethod 4: Whole First
SpeedMediumFastFastFastest (when applicable)
Best forAll fractionsProper fractionsMixed numbersMixed numbers with different wholes
Skill neededFinding LCDMultiplicationDivisionWhole number comparison
Works with negativesYesCautionYesYes
RecommendationBest defaultQuick shortcutMost intuitiveMixed numbers only

Special Cases

Equal values, negatives, zero, and improper fractions

These cases require a little more care because the most obvious visual comparison can be misleading.

Special Case

Equal values

Different-looking fractions can represent the same amount.

Rule: Simplify or convert both fractions, then use the equals symbol when the values match.

2/4 vs 1/2

  1. 1.Simplify 2/4 to 1/2.
  2. 2.Both values are now 1/2.
  3. 3.Use the equals symbol.

Answer: 2/4 = 1/2

Special Case

Negative fractions

The value closer to zero is greater.

Rule: Convert to decimals or use a number line for the clearest negative comparison.

-1/2 vs -3/4

  1. 1.-1/2 = -0.5.
  2. 2.-3/4 = -0.75.
  3. 3.-0.5 is closer to zero.

Answer: -1/2 > -3/4

With negative fractions, the rules flip. The fraction closer to zero is the greater value. Converting to decimals is often the clearest approach for negative comparisons.

Special Case

Zero numerator

A zero numerator makes the fraction equal to zero.

Rule: Any positive fraction is greater than zero.

0/5 vs 1/8

  1. 1.0/5 = 0.
  2. 2.1/8 is positive.
  3. 3.A positive fraction is greater than 0.

Answer: 0/5 < 1/8

Special Case

Improper vs mixed

Put both values in a comparable format first.

Rule: Convert the improper fraction to a mixed number, or convert the mixed number to an improper fraction.

7/4 vs 1 3/4

  1. 1.Convert 7/4 to 1 3/4.
  2. 2.Both values are 1 3/4.
  3. 3.Use the equals symbol.

Answer: 7/4 = 1 3/4

Built-in Calculator

Try the fraction comparator

Enter two fractions or mixed numbers below to see which is greater, with the full step-by-step comparison.

Instant Comparator

Compare two fractions or mixed numbers instantly

Enter two fractions or mixed numbers to see which is greater, with full step-by-step reasoning.

Instant Comparator

Enter two fractions or mixed numbers to compare values with a cross-check and full step-by-step reasoning.

Left value

Enter a whole part and a fraction.

Use +/- or drag a field sideways to adjust quickly.

Right value

Enter a whole part and a fraction.

Use +/- or drag a field sideways to adjust quickly.

FAQ

Compare fractions FAQ

How do you compare two fractions?

Convert them to a common denominator, compare the numerators, and then write the correct comparison symbol between the original fractions.

What is the fastest way to compare fractions?

For positive fractions, cross multiplication is usually fastest. For a classroom default, common denominators are the most reliable.

How do you compare mixed numbers?

Compare the whole-number parts first. If they are equal, compare the fraction parts with common denominators, cross multiplication, or decimals.

Continue Learning

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Extend pairwise comparison into sorting from least to greatest.

Mixed Number to Decimal

Use decimal conversion as an intuitive comparison method.

Fraction to Decimal

Practice the decimal method for proper and improper fractions.

Mixed Number Calculator

Return to the main tool for mixed-number operations and conversions.