Is 3/10 Bigger Than 4/11?

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 \(\frac{3}{10}\): multiply numerator and denominator by 11.
  \[\frac{3}{10} = \frac{3 \times 11}{10 \times 11} = \frac{33}{110}\]
• Step 2. Convert \(\frac{4}{11}\): multiply numerator and denominator by 10.
  \[\frac{4}{11} = \frac{4 \times 10}{11 \times 10} = \frac{40}{110}\]
• Step 3. Compare the numerators: 33 vs 40.
• Step 4. Since 33 is less than 40, we know that \(\frac{3}{10} < \frac{4}{11}\).

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: \(4 \times 10 = 40\).
• Step 3. Compare the products: \(33 < 40\), so \(\frac{3}{10} < \frac{4}{11}\).

Method 3: Decimal Comparison

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

Since 0.3 is less than 0.363636, we confirm that \(\frac{3}{10} < \frac{4}{11}\). In percentage terms, \(\frac{3}{10}\) is 30% and \(\frac{4}{11}\) is 36.3636%, a difference of 6.3636 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 33 pieces vs 40 pieces is a straightforward comparison.