Is 5/6 Bigger Than 3/11?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 6 and 11, and the least common denominator (LCD) is 66.

• Step 1. Convert \(\frac{5}{6}\): multiply numerator and denominator by 11.
  \[\frac{5}{6} = \frac{5 \times 11}{6 \times 11} = \frac{55}{66}\]
• Step 2. Convert \(\frac{3}{11}\): multiply numerator and denominator by 6.
  \[\frac{3}{11} = \frac{3 \times 6}{11 \times 6} = \frac{18}{66}\]
• Step 3. Compare the numerators: 55 vs 18.
• Step 4. Since 55 is greater than 18, we know that \(\frac{5}{6} > \frac{3}{11}\).

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: \(5 \times 11 = 55\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(3 \times 6 = 18\).
• Step 3. Compare the products: \(55 > 18\), so \(\frac{5}{6} > \frac{3}{11}\).

Method 3: Decimal Comparison

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

Since 0.833333 is greater than 0.272727, we confirm that \(\frac{5}{6} > \frac{3}{11}\). In percentage terms, \(\frac{5}{6}\) is 83.3333% and \(\frac{3}{11}\) is 27.2727%, a difference of 56.0606 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 66, we're cutting both quantities into equal-sized pieces. Then 55 pieces vs 18 pieces is a straightforward comparison.