Understanding the Benchmark
A benchmark comparison checks fractions against useful reference points. Here the core statement is 2/3 > 2/5. The tool does more than say true or false. It shows why the statement is true. It also shows the size of the gap, the decimal forms, percent forms, and cross products. This helps students see the same idea in several ways.
Why 2/3 Is Greater
Both fractions start with the same numerator. Each has two parts selected. The difference is the denominator. Thirds divide a whole into three equal pieces. Fifths divide a whole into five equal pieces. One third is larger than one fifth. So two thirds must be larger than two fifths. The calculator confirms this with exact arithmetic.
Benchmark Method
A benchmark is a friendly value used for checking. One half is a common benchmark. The fraction 2/3 is above one half. The fraction 2/5 is below one half. That quick check already suggests 2/3 is greater. The tool also compares both values to any benchmark fraction you enter. This is useful when teaching number sense.
Cross Product Check
The calculator multiplies the first numerator by the second denominator. It also multiplies the second numerator by the first denominator. For 2/3 and 2/5, the products are 10 and 6. Since 10 is greater than 6, 2/3 is greater than 2/5. This method avoids decimal rounding.
Common Denominator View
The common denominator method rewrites both fractions with matching bottoms. The least common denominator of 3 and 5 is 15. So 2/3 becomes 10/15. The fraction 2/5 becomes 6/15. Now the comparison is simple. Ten fifteenths is greater than six fifteenths.
Reading the Result
A positive gap means the first fraction is larger. A negative gap means the second fraction is larger. A zero gap means fractions are equal. The percent gap is helpful when the difference must be explained in practical terms.
Practical Uses
Use this calculator for homework checks, worksheet building, tutoring, and quick classroom demonstrations. It is also useful for adult learning and review. CSV export helps store results in a spreadsheet. PDF export creates a neat summary for printing. The example table gives ready test cases. Always check that denominators are not zero before comparing.