Is 2/3 Bigger Than 1/4?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 3 and 4, 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. Convert \(\frac{1}{4}\): multiply numerator and denominator by 3.
  \[\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\]
• Step 3. Compare the numerators: 8 vs 3.
• Step 4. Since 8 is greater than 3, we know that \(\frac{2}{3} > \frac{1}{4}\).

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: \(2 \times 4 = 8\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(1 \times 3 = 3\).
• Step 3. Compare the products: \(8 > 3\), so \(\frac{2}{3} > \frac{1}{4}\).

Method 3: Decimal Comparison

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

Since 0.666667 is greater than 0.25, we confirm that \(\frac{2}{3} > \frac{1}{4}\). In percentage terms, \(\frac{2}{3}\) is 66.6667% and \(\frac{1}{4}\) is 25%, a difference of 41.6667 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 3 pieces is a straightforward comparison.