No, \(\frac{5}{7}\) < \(\frac{7}{8}\)
To compare these fractions, we need a common denominator. The denominators are 7 and 8, and the least common denominator (LCD) is 56.
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 0.714286 is less than 0.875, we confirm that \(\frac{5}{7} < \frac{7}{8}\). In percentage terms, \(\frac{5}{7}\) is 71.4286% and \(\frac{7}{8}\) is 87.5%, a difference of 16.0714 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 56, we're cutting both quantities into equal-sized pieces. Then 40 pieces vs 49 pieces is a straightforward comparison.
\(\frac{7}{8}\) is bigger. As a decimal, \(\frac{7}{8}\) = 0.875 while \(\frac{5}{7}\) = 0.714286.
The difference is \(\frac{9}{56}\), which equals 0.160714 in decimal form (16.0714 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 \(\frac{7}{8}\) \(>\) \(\frac{5}{7}\).