Is 1/10 Bigger Than 2/11?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 10 and 11, and the least common denominator (LCD) is 110.

• Step 1. Convert \(\frac{1}{10}\): multiply numerator and denominator by 11.
  \[\frac{1}{10} = \frac{1 \times 11}{10 \times 11} = \frac{11}{110}\]
• Step 2. Convert \(\frac{2}{11}\): multiply numerator and denominator by 10.
  \[\frac{2}{11} = \frac{2 \times 10}{11 \times 10} = \frac{20}{110}\]
• Step 3. Compare the numerators: 11 vs 20.
• Step 4. Since 11 is less than 20, we know that \(\frac{1}{10} < \frac{2}{11}\).

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: \(2 \times 10 = 20\).
• Step 3. Compare the products: \(11 < 20\), so \(\frac{1}{10} < \frac{2}{11}\).

Method 3: Decimal Comparison

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

Since 0.1 is less than 0.181818, we confirm that \(\frac{1}{10} < \frac{2}{11}\). In percentage terms, \(\frac{1}{10}\) is 10% and \(\frac{2}{11}\) is 18.1818%, a difference of 8.1818 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 110, we're cutting both quantities into equal-sized pieces. Then 11 pieces vs 20 pieces is a straightforward comparison.