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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{7}{8}\) and \(\frac{7}{9}\) 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 0.875 is greater than 0.777778, we confirm that \(\frac{7}{8} > \frac{7}{9}\). In percentage terms, \(\frac{7}{8}\) is 87.5% and \(\frac{7}{9}\) is 77.7778%, a difference of 9.7222 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, \(\frac{7}{8}\) is the bigger fraction even though both have 7 in the numerator.
\(\frac{7}{8}\) is bigger. As a decimal, \(\frac{7}{8}\) = 0.875 while \(\frac{7}{9}\) = 0.777778.
The difference is \(\frac{7}{72}\), which equals 0.097222 in decimal form (9.7222 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 \(\frac{7}{8}\) \(>\) \(\frac{7}{9}\).