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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{5}{8}\) and \(\frac{5}{9}\) is straightforward once you know the right approach. Below we walk through three proven methods for comparing fractions: finding a common denominator, cross multiplication, and converting to decimals. Each method will give you the same answer, so choose the one that feels easiest.
To compare these fractions, we need a common denominator. The denominators are 8 and 9, and the least common denominator (LCD) is 72.
A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:
Convert each fraction to a decimal by dividing the numerator by the denominator:
Since 0.625 is greater than 0.555556, we confirm that \(\frac{5}{8} > \frac{5}{9}\). In percentage terms, \(\frac{5}{8}\) is 62.5% and \(\frac{5}{9}\) is 55.5556%, a difference of 6.9444 percentage points.
When two fractions have the same numerator, you have the same number of pieces — but the pieces are different sizes. A smaller denominator means each piece is larger. Since 8ths are larger pieces than 9ths, \(\frac{5}{8}\) is the bigger fraction even though both have 5 in the numerator.
\(\frac{5}{8}\) is bigger. As a decimal, \(\frac{5}{8}\) = 0.625 while \(\frac{5}{9}\) = 0.555556.
The difference is \(\frac{5}{72}\), which equals 0.069444 in decimal form (6.9444 percentage points).
You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that \(\frac{5}{8}\) \(>\) \(\frac{5}{9}\).