No, \(\frac{4}{7}\) < \(\frac{6}{7}\)
These fractions already share the same denominator: 7. 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 0.571429 is less than 0.857143, we confirm that \(\frac{4}{7} < \frac{6}{7}\). In percentage terms, \(\frac{4}{7}\) is 57.1429% and \(\frac{6}{7}\) is 85.7143%, a difference of 28.5714 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 6 pieces is more than 4 pieces of the same size, \(\frac{6}{7}\) is the larger fraction.
\(\frac{6}{7}\) is bigger. As a decimal, \(\frac{6}{7}\) = 0.857143 while \(\frac{4}{7}\) = 0.571429.
The difference is \(\frac{2}{7}\), which equals 0.285714 in decimal form (28.5714 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 \(\frac{6}{7}\) \(>\) \(\frac{4}{7}\).