No, \(\frac{3}{11}\) < \(\frac{7}{11}\)
These fractions already share the same denominator: 11. 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 0.272727 is less than 0.636364, we confirm that \(\frac{3}{11} < \frac{7}{11}\). In percentage terms, \(\frac{3}{11}\) is 27.2727% and \(\frac{7}{11}\) is 63.6364%, a difference of 36.3636 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 7 pieces is more than 3 pieces of the same size, \(\frac{7}{11}\) is the larger fraction.
\(\frac{7}{11}\) is bigger. As a decimal, \(\frac{7}{11}\) = 0.636364 while \(\frac{3}{11}\) = 0.272727.
The difference is \(\frac{4}{11}\), which equals 0.363636 in decimal form (36.3636 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 \(\frac{7}{11}\) \(>\) \(\frac{3}{11}\).