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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{1}{10}\) and \(\frac{3}{10}\) 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.
These fractions already share the same denominator: 10. We just need to compare the numerators.
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 0.1 is less than 0.3, we confirm that \(\frac{1}{10} < \frac{3}{10}\). In percentage terms, \(\frac{1}{10}\) is 10% and \(\frac{3}{10}\) is 30%, a difference of 20 percentage points.
When two fractions share the same denominator, the pieces are the same size. A fraction with more pieces (a larger numerator) is simply a larger amount. Since 3 pieces is more than 1 pieces of the same size, \(\frac{3}{10}\) is the larger fraction.
\(\frac{3}{10}\) is bigger. As a decimal, \(\frac{3}{10}\) = 0.3 while \(\frac{1}{10}\) = 0.1.
The difference is \(\frac{1}{5}\), which equals 0.2 in decimal form (20 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 \(\frac{3}{10}\) \(>\) \(\frac{1}{10}\).