No, \(\frac{1}{3}\) < \(\frac{2}{3}\)
These fractions already share the same denominator: 3. 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 0.333333 is less than 0.666667, we confirm that \(\frac{1}{3} < \frac{2}{3}\). In percentage terms, \(\frac{1}{3}\) is 33.3333% and \(\frac{2}{3}\) is 66.6667%, a difference of 33.3333 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 2 pieces is more than 1 pieces of the same size, \(\frac{2}{3}\) is the larger fraction.
\(\frac{2}{3}\) is bigger. As a decimal, \(\frac{2}{3}\) = 0.666667 while \(\frac{1}{3}\) = 0.333333.
The difference is \(\frac{1}{3}\), which equals 0.333333 in decimal form (33.3333 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 \(\frac{2}{3}\) \(>\) \(\frac{1}{3}\).