Is 2/3 Bigger Than 1/6?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 3 and 6, and the least common denominator (LCD) is 6.

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

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: \(2 \times 6 = 12\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(1 \times 3 = 3\).
• Step 3. Compare the products: \(12 > 3\), so \(\frac{2}{3} > \frac{1}{6}\).

Method 3: Decimal Comparison

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

Since 0.666667 is greater than 0.166667, we confirm that \(\frac{2}{3} > \frac{1}{6}\). In percentage terms, \(\frac{2}{3}\) is 66.6667% and \(\frac{1}{6}\) is 16.6667%, a difference of 50 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 6, we're cutting both quantities into equal-sized pieces. Then 4 pieces vs 1 pieces is a straightforward comparison.