Is 1/3 Bigger Than 7/8?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 3 and 8, and the least common denominator (LCD) is 24.

• Step 1. Convert \(\frac{1}{3}\): multiply numerator and denominator by 8.
  \[\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}\]
• Step 2. Convert \(\frac{7}{8}\): multiply numerator and denominator by 3.
  \[\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\]
• Step 3. Compare the numerators: 8 vs 21.
• Step 4. Since 8 is less than 21, we know that \(\frac{1}{3} < \frac{7}{8}\).

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: \(7 \times 3 = 21\).
• Step 3. Compare the products: \(8 < 21\), so \(\frac{1}{3} < \frac{7}{8}\).

Method 3: Decimal Comparison

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

Since 0.333333 is less than 0.875, we confirm that \(\frac{1}{3} < \frac{7}{8}\). In percentage terms, \(\frac{1}{3}\) is 33.3333% and \(\frac{7}{8}\) is 87.5%, a difference of 54.1667 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 24, we're cutting both quantities into equal-sized pieces. Then 8 pieces vs 21 pieces is a straightforward comparison.