No, \(\frac{5}{8}\) < \(\frac{7}{8}\)
These fractions already share the same denominator: 8. 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 0.625 is less than 0.875, we confirm that \(\frac{5}{8} < \frac{7}{8}\). In percentage terms, \(\frac{5}{8}\) is 62.5% and \(\frac{7}{8}\) is 87.5%, a difference of 25 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 7 pieces is more than 5 pieces of the same size, \(\frac{7}{8}\) is the larger fraction.
\(\frac{7}{8}\) is bigger. As a decimal, \(\frac{7}{8}\) = 0.875 while \(\frac{5}{8}\) = 0.625.
The difference is \(\frac{1}{4}\), which equals 0.25 in decimal form (25 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 \(\frac{7}{8}\) \(>\) \(\frac{5}{8}\).