Is 1/11 Bigger Than 1/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 11 and 12, and the least common denominator (LCD) is 132.

• Step 1. Convert \(\frac{1}{11}\): multiply numerator and denominator by 12.
  \[\frac{1}{11} = \frac{1 \times 12}{11 \times 12} = \frac{12}{132}\]
• Step 2. Convert \(\frac{1}{12}\): multiply numerator and denominator by 11.
  \[\frac{1}{12} = \frac{1 \times 11}{12 \times 11} = \frac{11}{132}\]
• Step 3. Compare the numerators: 12 vs 11.
• Step 4. Since 12 is greater than 11, we know that \(\frac{1}{11} > \frac{1}{12}\).

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: \(1 \times 12 = 12\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(1 \times 11 = 11\).
• Step 3. Compare the products: \(12 > 11\), so \(\frac{1}{11} > \frac{1}{12}\).

Method 3: Decimal Comparison

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

Since 0.090909 is greater than 0.083333, we confirm that \(\frac{1}{11} > \frac{1}{12}\). In percentage terms, \(\frac{1}{11}\) is 9.0909% and \(\frac{1}{12}\) is 8.3333%, a difference of 0.7576 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 11ths, \(\frac{1}{11}\) is the bigger fraction even though both have 1 in the numerator.