The short answer

Use the denominator, cross multiplication, benchmark values, or exact conversion depending on the numbers. For two positive fractions with nonzero denominators, cross multiplication gives a dependable comparison without rounding. The important rule is to compare values, not just the size of the numerator or denominator.

Method 1: Same denominator

When denominators match, compare numerators directly:

5/9 vs 7/9

Both pieces describe ninths. Seven ninths is greater than five ninths, so 7/9 > 5/9.

Method 2: Cross multiplication

For a/b and c/d, compare a × d with c × b when the denominators are positive.

Example:

3/4 vs 5/8
3 × 8 = 24
5 × 4 = 20

Because 24 is greater than 20, 3/4 > 5/8. This avoids decimal rounding and works well when the denominators are different.

Method 3: Use a benchmark

Ask whether each fraction is close to a familiar value such as 0, 1/2, or 1.

For 5/12 and 7/12, both have the same denominator, but a benchmark can still help explain the size: 5/12 is below one-half and 7/12 is above one-half. This explanation is often easier for a student to remember than a rule alone.

Method 4: Convert carefully

You can convert fractions to decimals or percentages when the context calls for it. For example, 1/4 = 0.25 and 3/4 = 0.75. Use enough precision for repeating decimals, and do not let a rounded display decide a close comparison when an exact method is available.

Mixed numbers and negative fractions

Convert mixed numbers into improper fractions or compare their whole-number parts first. For negative values, remember that the value closer to zero is greater:

-2/5 > -3/5

The calculator can compare mixed numbers, integers, and negative fractions with exact arithmetic, but the explanation still matters: enter the values as written, inspect the result, and confirm the sign.

A practical checking workflow

  1. Rewrite both values clearly, including negative signs and mixed-number parts.
  2. Check whether the denominators are the same.
  3. If not, use cross multiplication or a benchmark.
  4. Use the calculator to verify the relationship and view the steps.
  5. Explain the result in a sentence, not only with >, <, or =.

Common mistakes

  • Assuming the fraction with the larger denominator is larger.
  • Comparing numerators while ignoring the denominators.
  • Forgetting that multiplying an inequality by a negative value reverses its direction.
  • Rounding two close decimals too early.
  • Treating a mixed number as if its numerator were the whole value.

Source and method note

The school-level comparison methods are consistent with OpenStax Prealgebra: Compare and Order Fractions. The site uses exact arithmetic for its supported inputs; this is a calculation feature, not a claim that a calculator replaces instruction.

Tool link: https://www.comparingfractions.com/

Suggested visual: an original worked example showing 3/4 and 5/8, their cross products, and the final number-line position.