Is 3/5 Bigger Than 5/6?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 6, and the least common denominator (LCD) is 30.

• Step 1. Convert \(\frac{3}{5}\): multiply numerator and denominator by 6.
  \[\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}\]
• Step 2. Convert \(\frac{5}{6}\): multiply numerator and denominator by 5.
  \[\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\]
• Step 3. Compare the numerators: 18 vs 25.
• Step 4. Since 18 is less than 25, we know that \(\frac{3}{5} < \frac{5}{6}\).

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: \(3 \times 6 = 18\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(5 \times 5 = 25\).
• Step 3. Compare the products: \(18 < 25\), so \(\frac{3}{5} < \frac{5}{6}\).

Method 3: Decimal Comparison

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

Since 0.6 is less than 0.833333, we confirm that \(\frac{3}{5} < \frac{5}{6}\). In percentage terms, \(\frac{3}{5}\) is 60% and \(\frac{5}{6}\) is 83.3333%, a difference of 23.3333 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 30, we're cutting both quantities into equal-sized pieces. Then 18 pieces vs 25 pieces is a straightforward comparison.