Is 1/5 Bigger Than 5/8?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 8, and the least common denominator (LCD) is 40.

• Step 1. Convert \(\frac{1}{5}\): multiply numerator and denominator by 8.
  \[\frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40}\]
• Step 2. Convert \(\frac{5}{8}\): multiply numerator and denominator by 5.
  \[\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}\]
• Step 3. Compare the numerators: 8 vs 25.
• Step 4. Since 8 is less than 25, we know that \(\frac{1}{5} < \frac{5}{8}\).

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: \(1 \times 8 = 8\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(5 \times 5 = 25\).
• Step 3. Compare the products: \(8 < 25\), so \(\frac{1}{5} < \frac{5}{8}\).

Method 3: Decimal Comparison

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

Since 0.2 is less than 0.625, we confirm that \(\frac{1}{5} < \frac{5}{8}\). In percentage terms, \(\frac{1}{5}\) is 20% and \(\frac{5}{8}\) is 62.5%, a difference of 42.5 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 40, we're cutting both quantities into equal-sized pieces. Then 8 pieces vs 25 pieces is a straightforward comparison.