Is 1/2 Bigger Than 3/4?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 2 and 4, and the least common denominator (LCD) is 4.

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

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

Method 3: Decimal Comparison

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

Since 0.5 is less than 0.75, we confirm that \(\frac{1}{2} < \frac{3}{4}\). In percentage terms, \(\frac{1}{2}\) is 50% and \(\frac{3}{4}\) is 75%, 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 4, we're cutting both quantities into equal-sized pieces. Then 2 pieces vs 3 pieces is a straightforward comparison.