No, \(\frac{1}{3}\) < \(\frac{5}{7}\)
To compare these fractions, we need a common denominator. The denominators are 3 and 7, and the least common denominator (LCD) is 21.
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 0.714286, we confirm that \(\frac{1}{3} < \frac{5}{7}\). In percentage terms, \(\frac{1}{3}\) is 33.3333% and \(\frac{5}{7}\) is 71.4286%, a difference of 38.0952 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 21, we're cutting both quantities into equal-sized pieces. Then 7 pieces vs 15 pieces is a straightforward comparison.
\(\frac{5}{7}\) is bigger. As a decimal, \(\frac{5}{7}\) = 0.714286 while \(\frac{1}{3}\) = 0.333333.
The difference is \(\frac{8}{21}\), which equals 0.380952 in decimal form (38.0952 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 \(\frac{5}{7}\) \(>\) \(\frac{1}{3}\).