Is 2/5 Bigger Than 2/7?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 7, and the least common denominator (LCD) is 35.

• Step 1. Convert \(\frac{2}{5}\): multiply numerator and denominator by 7.
  \[\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}\]
• Step 2. Convert \(\frac{2}{7}\): multiply numerator and denominator by 5.
  \[\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}\]
• Step 3. Compare the numerators: 14 vs 10.
• Step 4. Since 14 is greater than 10, we know that \(\frac{2}{5} > \frac{2}{7}\).

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: \(2 \times 7 = 14\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(2 \times 5 = 10\).
• Step 3. Compare the products: \(14 > 10\), so \(\frac{2}{5} > \frac{2}{7}\).

Method 3: Decimal Comparison

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

Since 0.4 is greater than 0.285714, we confirm that \(\frac{2}{5} > \frac{2}{7}\). In percentage terms, \(\frac{2}{5}\) is 40% and \(\frac{2}{7}\) is 28.5714%, a difference of 11.4286 percentage points.

Why Does This Work?

When two fractions have the same numerator, you have the same number of pieces — but the pieces are different sizes. A smaller denominator means each piece is larger. Since 7ths are larger pieces than 5ths, \(\frac{2}{5}\) is the bigger fraction even though both have 2 in the numerator.