Is 2/5 Bigger Than 7/11?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 11, and the least common denominator (LCD) is 55.

• Step 1. Convert \(\frac{2}{5}\): multiply numerator and denominator by 11.
  \[\frac{2}{5} = \frac{2 \times 11}{5 \times 11} = \frac{22}{55}\]
• Step 2. Convert \(\frac{7}{11}\): multiply numerator and denominator by 5.
  \[\frac{7}{11} = \frac{7 \times 5}{11 \times 5} = \frac{35}{55}\]
• Step 3. Compare the numerators: 22 vs 35.
• Step 4. Since 22 is less than 35, we know that \(\frac{2}{5} < \frac{7}{11}\).

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: \(2 \times 11 = 22\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 5 = 35\).
• Step 3. Compare the products: \(22 < 35\), so \(\frac{2}{5} < \frac{7}{11}\).

Method 3: Decimal Comparison

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

Since 0.4 is less than 0.636364, we confirm that \(\frac{2}{5} < \frac{7}{11}\). In percentage terms, \(\frac{2}{5}\) is 40% and \(\frac{7}{11}\) is 63.6364%, a difference of 23.6364 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 55, we're cutting both quantities into equal-sized pieces. Then 22 pieces vs 35 pieces is a straightforward comparison.