No, \(\frac{4}{5}\) < \(\frac{9}{11}\)
To compare these fractions, we need a common denominator. The denominators are 5 and 11, and the least common denominator (LCD) is 55.
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 less than 0.818182, we confirm that \(\frac{4}{5} < \frac{9}{11}\). In percentage terms, \(\frac{4}{5}\) is 80% and \(\frac{9}{11}\) is 81.8182%, a difference of 1.8182 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 55, we're cutting both quantities into equal-sized pieces. Then 44 pieces vs 45 pieces is a straightforward comparison.
\(\frac{9}{11}\) is bigger. As a decimal, \(\frac{9}{11}\) = 0.818182 while \(\frac{4}{5}\) = 0.8.
The difference is \(\frac{1}{55}\), which equals 0.018182 in decimal form (1.8182 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 \(\frac{9}{11}\) \(>\) \(\frac{4}{5}\).