Compare & Order Fractions
Compare and order up to four fractions from smallest to largest, showing decimal equivalents and the LCD. Leave unused fields at 0.
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How to use this calculator
- 1
Enter up to four fractions — numerator and denominator for each. Set numerator to 0 to skip a slot.
- 2
The fractions are ordered from smallest to largest with their decimal values.
- 3
The LCD is computed and each fraction is rewritten with the LCD as denominator.
Frequently asked questions
How do you compare two fractions?
The quickest way: convert both to decimals (divide numerator by denominator) and compare. For exact comparison without decimals: find the LCD and compare the numerators with that common denominator. Cross-multiplication also works: compare a/b and c/d by comparing a×d with b×c.
What is the LCD?
The LCD (Least Common Denominator) is the smallest positive integer divisible by all denominators. It is the LCM (Least Common Multiple) of the denominators. To add fractions, you first convert them to the LCD. For comparing, the LCD lets you directly compare numerators: whichever is larger has the larger fraction.
Why is 1/3 less than 1/2 even though 3 > 2?
A larger denominator means each piece is smaller (the whole is divided into more parts). 1/3 takes one of three pieces; 1/2 takes one of two larger pieces. As denominator increases (for unit fractions 1/n), the fraction decreases: 1/2 > 1/3 > 1/4 > 1/5 > …
What is cross-multiplication?
To compare a/b and c/d without finding the LCD: compute a×d and b×c. If a×d > b×c then a/b > c/d; if equal they are equivalent fractions. For 3/4 vs 2/3: 3×3=9, 4×2=8; since 9>8, then 3/4 > 2/3. Cross-multiplication is the fastest two-fraction comparison and is exactly what the LCD method computes under the hood.
Compare and order fractions using LCD and decimal conversion
Three methods for comparing fractions
Method 1 — Decimal conversion: divide each numerator by its denominator and compare the results. Fast and always works but introduces rounding for repeating decimals. Method 2 — LCD method: find the Least Common Denominator, convert all fractions, then compare numerators directly. Exact and useful for adding fractions afterward. Method 3 — Cross-multiplication: for two fractions a/b and c/d, compare a×d with b×c. Fast and exact for pairs.
Finding the LCD efficiently
The LCD of two denominators a and b is LCM(a, b) = a×b / GCD(a, b). For multiple denominators, compute pairwise: LCD(2, 3, 4) = LCM(LCM(2,3), 4) = LCM(6, 4) = 12. The Euclidean algorithm makes each GCD step fast. For the denominators 4, 6, 8: LCD = LCM(4, LCM(6, 8)) = LCM(4, 24) = 24.
Ordering fractions in everyday contexts
Comparing fractions arises when comparing discounts (20% off vs ¼ off vs 1/6 off), recipe scaling (is ¾ cup more or less than 5/8 cup?), and probability (which event is more likely: 3/10 or 7/25?). Converting to decimals resolves all of these quickly, but the LCD method is preferred in education because it reinforces fraction equivalence and prepares students for fraction addition and subtraction.
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