🔄 Want to compare different fractions? Change the numbers above and click Compare again.
Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{1}{5}\) and \(\frac{7}{10}\) 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 0.2 is less than 0.7, we confirm that \(\frac{1}{5} < \frac{7}{10}\). In percentage terms, \(\frac{1}{5}\) is 20% and \(\frac{7}{10}\) is 70%, a difference of 50 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 2 pieces vs 7 pieces is a straightforward comparison.
\(\frac{7}{10}\) is bigger. As a decimal, \(\frac{7}{10}\) = 0.7 while \(\frac{1}{5}\) = 0.2.
The difference is \(\frac{1}{2}\), which equals 0.5 in decimal form (50 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 \(\frac{7}{10}\) \(>\) \(\frac{1}{5}\).