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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{1}{7}\) and \(\frac{1}{10}\) 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 7 and 10, and the least common denominator (LCD) is 70.
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 0.142857 is greater than 0.1, we confirm that \(\frac{1}{7} > \frac{1}{10}\). In percentage terms, \(\frac{1}{7}\) is 14.2857% and \(\frac{1}{10}\) is 10%, a difference of 4.2857 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 7ths are larger pieces than 10ths, \(\frac{1}{7}\) is the bigger fraction even though both have 1 in the numerator.
\(\frac{1}{7}\) is bigger. As a decimal, \(\frac{1}{7}\) = 0.142857 while \(\frac{1}{10}\) = 0.1.
The difference is \(\frac{3}{70}\), which equals 0.042857 in decimal form (4.2857 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 \(\frac{1}{7}\) \(>\) \(\frac{1}{10}\).