Yes, \(\frac{1}{5}\) > \(\frac{1}{7}\)
To compare these fractions, we need a common denominator. The denominators are 5 and 7, and the least common denominator (LCD) is 35.
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 greater than 0.142857, we confirm that \(\frac{1}{5} > \frac{1}{7}\). In percentage terms, \(\frac{1}{5}\) is 20% and \(\frac{1}{7}\) is 14.2857%, a difference of 5.7143 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 5ths, \(\frac{1}{5}\) is the bigger fraction even though both have 1 in the numerator.
\(\frac{1}{5}\) is bigger. As a decimal, \(\frac{1}{5}\) = 0.2 while \(\frac{1}{7}\) = 0.142857.
The difference is \(\frac{2}{35}\), which equals 0.057143 in decimal form (5.7143 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 \(\frac{1}{5}\) \(>\) \(\frac{1}{7}\).