Is 5/6 Bigger Than 5/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 6 and 12, and the least common denominator (LCD) is 12.

• Step 1. Convert \(\frac{5}{6}\): multiply numerator and denominator by 2.
  \[\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}\]
• Step 2. Keep \(\frac{5}{12}\) as it is — the denominator is already 12.
• Step 3. Compare the numerators: 10 vs 5.
• Step 4. Since 10 is greater than 5, we know that \(\frac{5}{6} > \frac{5}{12}\).

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: \(5 \times 12 = 60\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(5 \times 6 = 30\).
• Step 3. Compare the products: \(60 > 30\), so \(\frac{5}{6} > \frac{5}{12}\).

Method 3: Decimal Comparison

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

Since 0.833333 is greater than 0.416667, we confirm that \(\frac{5}{6} > \frac{5}{12}\). In percentage terms, \(\frac{5}{6}\) is 83.3333% and \(\frac{5}{12}\) is 41.6667%, a difference of 41.6667 percentage points.

Why Does This Work?

When two fractions have the same numerator, you have the same number of pieces — but the pieces are different sizes. A smaller denominator means each piece is larger. Since 12ths are larger pieces than 6ths, \(\frac{5}{6}\) is the bigger fraction even though both have 5 in the numerator.