No, \(\frac{1}{4}\) < \(\frac{6}{7}\)
To compare these fractions, we need a common denominator. The denominators are 4 and 7, and the least common denominator (LCD) is 28.
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 0.25 is less than 0.857143, we confirm that \(\frac{1}{4} < \frac{6}{7}\). In percentage terms, \(\frac{1}{4}\) is 25% and \(\frac{6}{7}\) is 85.7143%, a difference of 60.7143 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 28, we're cutting both quantities into equal-sized pieces. Then 7 pieces vs 24 pieces is a straightforward comparison.
\(\frac{6}{7}\) is bigger. As a decimal, \(\frac{6}{7}\) = 0.857143 while \(\frac{1}{4}\) = 0.25.
The difference is \(\frac{17}{28}\), which equals 0.607143 in decimal form (60.7143 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 \(\frac{6}{7}\) \(>\) \(\frac{1}{4}\).