Is 2/5 Bigger Than 3/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 10, and the least common denominator (LCD) is 10.

• Step 1. Convert \(\frac{2}{5}\): multiply numerator and denominator by 2.
  \[\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}\]
• Step 2. Keep \(\frac{3}{10}\) as it is — the denominator is already 10.
• Step 3. Compare the numerators: 4 vs 3.
• Step 4. Since 4 is greater than 3, we know that \(\frac{2}{5} > \frac{3}{10}\).

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: \(2 \times 10 = 20\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(3 \times 5 = 15\).
• Step 3. Compare the products: \(20 > 15\), so \(\frac{2}{5} > \frac{3}{10}\).

Method 3: Decimal Comparison

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

Since 0.4 is greater than 0.3, we confirm that \(\frac{2}{5} > \frac{3}{10}\). In percentage terms, \(\frac{2}{5}\) is 40% and \(\frac{3}{10}\) is 30%, a difference of 10 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 10, we're cutting both quantities into equal-sized pieces. Then 4 pieces vs 3 pieces is a straightforward comparison.