Is 1/6 Bigger Than 7/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 6 and 12, and the least common denominator (LCD) is 12.

• Step 1. Convert \(\frac{1}{6}\): multiply numerator and denominator by 2.
  \[\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}\]
• Step 2. Keep \(\frac{7}{12}\) as it is — the denominator is already 12.
• Step 3. Compare the numerators: 2 vs 7.
• Step 4. Since 2 is less than 7, we know that \(\frac{1}{6} < \frac{7}{12}\).

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: \(7 \times 6 = 42\).
• Step 3. Compare the products: \(12 < 42\), so \(\frac{1}{6} < \frac{7}{12}\).

Method 3: Decimal Comparison

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

Since 0.166667 is less than 0.583333, we confirm that \(\frac{1}{6} < \frac{7}{12}\). In percentage terms, \(\frac{1}{6}\) is 16.6667% and \(\frac{7}{12}\) is 58.3333%, 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 2 pieces vs 7 pieces is a straightforward comparison.