Is 3/4 Bigger Than 1/6?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 4 and 6, and the least common denominator (LCD) is 12.

• Step 1. Convert \(\frac{3}{4}\): multiply numerator and denominator by 3.
  \[\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\]
• Step 2. Convert \(\frac{1}{6}\): multiply numerator and denominator by 2.
  \[\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}\]
• Step 3. Compare the numerators: 9 vs 2.
• Step 4. Since 9 is greater than 2, we know that \(\frac{3}{4} > \frac{1}{6}\).

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: \(3 \times 6 = 18\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(1 \times 4 = 4\).
• Step 3. Compare the products: \(18 > 4\), so \(\frac{3}{4} > \frac{1}{6}\).

Method 3: Decimal Comparison

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

Since 0.75 is greater than 0.166667, we confirm that \(\frac{3}{4} > \frac{1}{6}\). In percentage terms, \(\frac{3}{4}\) is 75% and \(\frac{1}{6}\) is 16.6667%, a difference of 58.3333 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 9 pieces vs 2 pieces is a straightforward comparison.