No, \(\frac{1}{2}\) < \(\frac{4}{7}\)
To compare these fractions, we need a common denominator. The denominators are 2 and 7, and the least common denominator (LCD) is 14.
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 0.5 is less than 0.571429, we confirm that \(\frac{1}{2} < \frac{4}{7}\). In percentage terms, \(\frac{1}{2}\) is 50% and \(\frac{4}{7}\) is 57.1429%, a difference of 7.1429 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 14, we're cutting both quantities into equal-sized pieces. Then 7 pieces vs 8 pieces is a straightforward comparison.
\(\frac{4}{7}\) is bigger. As a decimal, \(\frac{4}{7}\) = 0.571429 while \(\frac{1}{2}\) = 0.5.
The difference is \(\frac{1}{14}\), which equals 0.071429 in decimal form (7.1429 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 \(\frac{4}{7}\) \(>\) \(\frac{1}{2}\).