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Compare 2 fractions using cross multiplication, common denominator, or decimal methods with detailed step-by-step solutions.
Best for: Quick comparisons of 2 fractions
Best for: Visual understanding and multiple fractions
Best for: Using calculators and estimating
Comparing fractions is a fundamental skill in mathematics that helps us understand relative sizes and order fractions from least to greatest.
When denominators are equal, simply compare the numerators. For example, 3/8 < 5/8 because 3 < 5.
When numerators are equal, the fraction with the smaller denominator is larger. For example, 2/3 > 2/5 because thirds are larger pieces than fifths.
Use benchmarks like 1/2, 1, or 0 to quickly estimate. For example, 5/9 is slightly more than 1/2, while 3/7 is slightly less than 1/2.
Cross multiplication is usually fastest for comparing just two fractions. However, if you need to order multiple fractions, finding a common denominator is more efficient. The decimal method is best when using a calculator.
Convert all fractions to the same denominator (LCD) or to decimals, then compare them all at once. You can also compare pairs using cross multiplication, but this takes longer with many fractions.
Cross multiplication works because when you multiply both fractions by the product of their denominators, you get equivalent fractions with the same denominator. Comparing these numerators tells you which original fraction was larger.
Yes! The same methods work. Remember that a negative fraction is less than a positive one. When comparing two negative fractions, the one closer to zero is larger (e.g., -1/2 > -3/4).
First compare the whole number parts. If they're equal, convert the fractional parts to the same denominator and compare. Alternatively, convert both mixed numbers to improper fractions and use any comparison method.
Use the decimal method for the most precise comparison, or find a common denominator. Cross multiplication also gives you exact results - even small differences in the products indicate which fraction is larger.