Fraction Addition & Subtraction
Practice fraction addition and subtraction with a free, browser-based math game. Includes step-by-step strategy, common mistakes, and classroom tips.
MathCompare Fractions
A bigger denominator does not mean a bigger fraction — a quarter is larger than a fifth. Below: the cross-multiplication trick that settles any comparison in one step, and the half-way benchmark that settles most of them without any arithmetic.
Choose your difficulty
Pick a level to start playing. You can switch at any time.
How to play
Compare the two fractions, then tap the larger one.
Tip: your progress and best score are saved in this browser only.
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MathWhat you are actually practicing
A larger denominator does not mean a larger fraction. A quarter is bigger than a fifth, and 7/8 is bigger than 3/4, even though 8 is larger than 4 and 7 is not that much larger than 3.
Comparing fractions is really comparing two divisions, and the only reliable way to do it quickly is cross-multiplication.
How the game works
You are shown two fractions and asked which is larger. Pick one; a wrong pick reveals the answer immediately.
Easy uses small denominators. Medium widens the set. Hard uses denominators that are close together, where estimating is not enough.
The relationships worth knowing
Cross-multiply: for 3/4 and 5/8, compute 3 × 8 = 24 and 5 × 4 = 20. Since 24 > 20, the first fraction is larger. Two multiplications, no common denominator.
Benchmark against a half: 3/4 is above a half, 5/8 is above a half too — but 3/5 is above and 2/5 below, which settles that pair instantly.
Same numerator, bigger denominator is smaller: 3/4 > 3/5 > 3/7. This one case covers a lot of questions.
Strategies that actually raise your score
Cross-multiply rather than convert. Finding a common denominator costs an extra step and an extra chance to slip. Multiplying the two diagonals gives the comparison directly.
Use the half-way benchmark first. If one fraction is above 1/2 and the other below, you are finished in one glance. Only when both are on the same side do you need the arithmetic.
Watch the denominator trap. The most common wrong answer is the fraction with the bigger denominator, chosen because the numbers look bigger. Slow down when the denominators differ a lot.
Check near-equality by cross-multiplying. When the two results are within a few units, you are dealing with a close pair — recompute rather than guessing.