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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{4}{5}\) 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 5 and 10, and the least common denominator (LCD) is 10.
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 0.8 is greater than 0.1, we confirm that \(\frac{4}{5} > \frac{1}{10}\). In percentage terms, \(\frac{4}{5}\) is 80% and \(\frac{1}{10}\) is 10%, a difference of 70 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 10, we're cutting both quantities into equal-sized pieces. Then 8 pieces vs 1 pieces is a straightforward comparison.
\(\frac{4}{5}\) is bigger. As a decimal, \(\frac{4}{5}\) = 0.8 while \(\frac{1}{10}\) = 0.1.
The difference is \(\frac{7}{10}\), which equals 0.7 in decimal form (70 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 \(\frac{4}{5}\) \(>\) \(\frac{1}{10}\).