Is 2/3 Bigger Than 11/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 3 and 12, and the least common denominator (LCD) is 12.

• Step 1. Convert \(\frac{2}{3}\): multiply numerator and denominator by 4.
  \[\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}\]
• Step 2. Keep \(\frac{11}{12}\) as it is — the denominator is already 12.
• Step 3. Compare the numerators: 8 vs 11.
• Step 4. Since 8 is less than 11, we know that \(\frac{2}{3} < \frac{11}{12}\).

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: \(2 \times 12 = 24\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(11 \times 3 = 33\).
• Step 3. Compare the products: \(24 < 33\), so \(\frac{2}{3} < \frac{11}{12}\).

Method 3: Decimal Comparison

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

Since 0.666667 is less than 0.916667, we confirm that \(\frac{2}{3} < \frac{11}{12}\). In percentage terms, \(\frac{2}{3}\) is 66.6667% and \(\frac{11}{12}\) is 91.6667%, a difference of 25 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 12, we're cutting both quantities into equal-sized pieces. Then 8 pieces vs 11 pieces is a straightforward comparison.