Is 1/8 Bigger Than 10/11?

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 \(\frac{1}{8}\): multiply numerator and denominator by 11.
  \[\frac{1}{8} = \frac{1 \times 11}{8 \times 11} = \frac{11}{88}\]
• Step 2. Convert \(\frac{10}{11}\): multiply numerator and denominator by 8.
  \[\frac{10}{11} = \frac{10 \times 8}{11 \times 8} = \frac{80}{88}\]
• Step 3. Compare the numerators: 11 vs 80.
• Step 4. Since 11 is less than 80, we know that \(\frac{1}{8} < \frac{10}{11}\).

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: \(1 \times 11 = 11\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(10 \times 8 = 80\).
• Step 3. Compare the products: \(11 < 80\), so \(\frac{1}{8} < \frac{10}{11}\).

Method 3: Decimal Comparison

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

Since 0.125 is less than 0.909091, we confirm that \(\frac{1}{8} < \frac{10}{11}\). In percentage terms, \(\frac{1}{8}\) is 12.5% and \(\frac{10}{11}\) is 90.9091%, a difference of 78.4091 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 11 pieces vs 80 pieces is a straightforward comparison.