Is 1/5 Bigger Than 1/6?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 6, and the least common denominator (LCD) is 30.

• Step 1. Convert \(\frac{1}{5}\): multiply numerator and denominator by 6.
  \[\frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}\]
• Step 2. Convert \(\frac{1}{6}\): multiply numerator and denominator by 5.
  \[\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}\]
• Step 3. Compare the numerators: 6 vs 5.
• Step 4. Since 6 is greater than 5, we know that \(\frac{1}{5} > \frac{1}{6}\).

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

Method 3: Decimal Comparison

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

Since 0.2 is greater than 0.166667, we confirm that \(\frac{1}{5} > \frac{1}{6}\). In percentage terms, \(\frac{1}{5}\) is 20% and \(\frac{1}{6}\) is 16.6667%, a difference of 3.3333 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 6ths are larger pieces than 5ths, \(\frac{1}{5}\) is the bigger fraction even though both have 1 in the numerator.