Picture this standard standardized test question: "Which fraction is greater: 4/7 or 5/9?" Standard classroom curriculum instructs students to list multiples of 7 and 9, find the common denominator (63), rewrite both fractions as equivalent fractions (36/63 vs 35/63), and then compare the numerators. While correct, this process takes upwards of two minutes. With the Cross-Multiplication Comparison Test, you can determine the winner in two seconds.
The 2-Second Upward Cross-Multiply Test
- Write the two fractions side by side:
4/7and5/9. - Multiply the bottom denominator of the right fraction (9) up into the top numerator of the left fraction (4):
9 × 4 = 36. Write 36 above4/7. - Multiply the bottom denominator of the left fraction (7) up into the top numerator of the right fraction (5):
7 × 5 = 35. Write 35 above5/9. - Compare the two numbers: 36 is greater than 35.
- Therefore: 4/7 > 5/9!
More Rapid Comparisons
Example 2: Compare 5/8 vs 7/11
- Left side:
11 × 5 = 55 - Right side:
8 × 7 = 56 - Since 56 > 55, 7/11 is greater than 5/8!
Example 3: Compare 3/4 vs 8/11
- Left side:
11 × 3 = 33 - Right side:
4 × 8 = 32 - Since 33 > 32, 3/4 is greater than 8/11!
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Frequently Asked Questions
Yes, but be careful with negative signs. Keep the negative sign attached to the numerator (e.g., -4/7 vs -5/9), then cross-multiply upwards. Remember that in negative numbers, a smaller negative value is greater.
Because you are scaling the numerators to have a shared common denominator. The product written at the top represents the scaled numerator.
Yes, you can use tournament-style pairwise comparisons to rank three or more fractions from least to greatest in seconds.