Is 5/6 Bigger Than 7/8?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 6 and 8, and the least common denominator (LCD) is 24.

• Step 1. Convert \(\frac{5}{6}\): multiply numerator and denominator by 4.
  \[\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\]
• Step 2. Convert \(\frac{7}{8}\): multiply numerator and denominator by 3.
  \[\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\]
• Step 3. Compare the numerators: 20 vs 21.
• Step 4. Since 20 is less than 21, we know that \(\frac{5}{6} < \frac{7}{8}\).

Method 2: Cross Multiplication

A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:

• Step 1. Multiply the numerator of the first fraction by the denominator of the second: \(5 \times 8 = 40\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 6 = 42\).
• Step 3. Compare the products: \(40 < 42\), so \(\frac{5}{6} < \frac{7}{8}\).

Method 3: Decimal Comparison

Convert each fraction to a decimal by dividing the numerator by the denominator:

Since 0.833333 is less than 0.875, we confirm that \(\frac{5}{6} < \frac{7}{8}\). In percentage terms, \(\frac{5}{6}\) is 83.3333% and \(\frac{7}{8}\) is 87.5%, a difference of 4.1667 percentage points.

Why Does This Work?

These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 24, we're cutting both quantities into equal-sized pieces. Then 20 pieces vs 21 pieces is a straightforward comparison.