Is 3/8 Bigger Than 6/11?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 8 and 11, and the least common denominator (LCD) is 88.

• Step 1. Convert \(\frac{3}{8}\): multiply numerator and denominator by 11.
  \[\frac{3}{8} = \frac{3 \times 11}{8 \times 11} = \frac{33}{88}\]
• Step 2. Convert \(\frac{6}{11}\): multiply numerator and denominator by 8.
  \[\frac{6}{11} = \frac{6 \times 8}{11 \times 8} = \frac{48}{88}\]
• Step 3. Compare the numerators: 33 vs 48.
• Step 4. Since 33 is less than 48, we know that \(\frac{3}{8} < \frac{6}{11}\).

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: \(3 \times 11 = 33\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(6 \times 8 = 48\).
• Step 3. Compare the products: \(33 < 48\), so \(\frac{3}{8} < \frac{6}{11}\).

Method 3: Decimal Comparison

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

Since 0.375 is less than 0.545455, we confirm that \(\frac{3}{8} < \frac{6}{11}\). In percentage terms, \(\frac{3}{8}\) is 37.5% and \(\frac{6}{11}\) is 54.5455%, a difference of 17.0455 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 88, we're cutting both quantities into equal-sized pieces. Then 33 pieces vs 48 pieces is a straightforward comparison.