Magnitude Comparison
Which quantity is larger?
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What is the Magnitude Comparison?
A magnitude comparison task shows two quantities and asks which one is larger. It is one of the simplest and most widely used tasks in numerical cognition research. A well-known finding is the numerical distance effect: people answer faster when the two values are far apart, such as 2 and 9, than when they are close, such as 7 and 8.
Researchers also use comparisons between fractions, decimals and percentages to study how flexibly people understand number size. A common difficulty is comparing fractions by their whole-number parts, for example assuming 1/8 is bigger than 1/5 because 8 is bigger than 5. The Neuroptimize Magnitude Comparison game starts with whole numbers and gradually mixes in fractions, decimals, percentages and short calculations.
How to play the Magnitude Comparison
- Two cards appear side by side. Tap the one with the bigger value. You have 45 seconds to make as many correct choices as you can.
- On a keyboard, press the left arrow to choose the left card and the right arrow to choose the right card.
- Choosing the smaller value counts as a mistake. After each choice the bigger card is highlighted, and for anything other than whole numbers the approximate values of both cards are shown.
- At the lowest levels you compare whole numbers. Fractions join from level 3, starting with pairs that share a numerator or a denominator.
- Fractions compared with decimals appear from level 8, percentages such as "30% of 80" from level 13, and calculations such as 12 × 4 or 3/4 of 36 from level 18.
- As your level rises, the two values get closer together. From level 8, some whole-number pairs differ only by two swapped digits, such as 6385 and 6358.
Strategies and tips
Same denominator, compare tops
When two fractions have the same denominator, the one with the bigger numerator is bigger: 5/7 beats 3/7. When they share a numerator, the smaller denominator wins: 2/5 beats 2/9, because the whole is cut into fewer, larger pieces.
Cross-multiply close fractions
For 5/8 against 7/11, multiply across: 5 × 11 = 55 and 7 × 8 = 56. The fraction whose numerator produced the bigger number is bigger, so 7/11 wins. This works for any pair of fractions and avoids converting to decimals.
Use benchmarks like one half
Compare each value with 1/2, 1/4 or 3/4 before calculating. 4/9 is just under a half and 0.53 is just over, so 0.53 is bigger. Benchmarks settle many pairs in one step.
Turn percentages into fractions
For "25% of 60", think a quarter of 60, which is 15. 10% is a tenth and 75% is three quarters. You can also swap the order: 30% of 80 equals 80% of 30, which is 24, so pick whichever is easier.
Scan digits from the left
For large whole numbers, compare the number of digits first, then the digits from left to right. With 6385 and 6358, the first difference is in the tens place: 8 beats 5. This avoids being caught by swapped-digit pairs.
The science behind the Magnitude Comparison
Magnitude comparison tasks ask which of two quantities is larger. Responses are faster when the values are far apart than when they are close, a pattern known as the numerical distance effect. Comparing values written in different formats, such as fractions and decimals, reflects the flexibility of number sense.
Frequently asked questions
What is the numerical distance effect?
It is the finding that people decide which of two numbers is larger more quickly when the numbers are far apart than when they are close together. It is one of the most consistent results in magnitude comparison research.
How do you quickly tell which fraction is bigger?
If the denominators match, compare the numerators. If the numerators match, the smaller denominator is bigger. Otherwise, cross-multiply or compare each fraction with a benchmark like one half.
Can the two values ever be equal?
No. The game compares values exactly as fractions, and it only shows pairs where one is strictly bigger. There is always one correct card.
Is Magnitude Comparison free?
Magnitude Comparison is a Pro game in Neuroptimize, and Pro starts with a 7-day free trial. Free players can also get it as the Pro game of the day in their daily workout.