No, \(\frac{2}{5}\) < \(\frac{3}{7}\)
To compare these fractions, we need a common denominator. The denominators are 5 and 7, and the least common denominator (LCD) is 35.
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 0.4 is less than 0.428571, we confirm that \(\frac{2}{5} < \frac{3}{7}\). In percentage terms, \(\frac{2}{5}\) is 40% and \(\frac{3}{7}\) is 42.8571%, a difference of 2.8571 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 35, we're cutting both quantities into equal-sized pieces. Then 14 pieces vs 15 pieces is a straightforward comparison.
\(\frac{3}{7}\) is bigger. As a decimal, \(\frac{3}{7}\) = 0.428571 while \(\frac{2}{5}\) = 0.4.
The difference is \(\frac{1}{35}\), which equals 0.028571 in decimal form (2.8571 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 \(\frac{3}{7}\) \(>\) \(\frac{2}{5}\).