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Cross Multiplication Visualizer
See the cross-multiplication method in action. Understand why multiplying the numerator of each fraction by the denominator of the other reveals which fraction is larger.
Quick Tips
- Cross-multiply: numerator of fraction A × denominator of fraction B versus denominator of fraction A × numerator of fraction B
- The larger cross-product belongs to the larger fraction
- Equal cross-products mean the fractions are equivalent
- This is the fastest way to compare two fractions without finding a common denominator
Understanding Cross Multiplication
The Formula
For fractions a/b and c/d, compute a×d and b×c. If a×d > b×c, then a/b > c/d. If a×d < b×c, then a/b < c/d. If a×d = b×c, the fractions are equivalent.
The x-Shape Method
Draw an X between the two fractions: multiply up-left to down-right, then down-left to up-right. Compare the two products. This visual X shape gives the technique its name and makes it easy to remember.
Frequently Asked Questions
Common questions about cross multiplication
Cross multiplication is a technique for comparing two fractions by multiplying the numerator of each fraction by the denominator of the other. If a/b and c/d are fractions, cross multiplication compares a×d versus b×c. The fraction with the larger cross product is the larger fraction.
Cross multiplication works because it implicitly converts both fractions to a common denominator (b×d) without actually computing it. The cross products a×d and c×b are the numerators you would get if you converted both fractions to denominator b×d. Comparing these numerators tells you which fraction is larger.
Use cross multiplication when you just need to know which of two fractions is larger. Use the common denominator method when you need to understand by how much, or when comparing more than two fractions. Cross multiplication is the fastest method for quick comparison of two fractions.