Is 7/8 Bigger Than 8/11?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 8 and 11, and the least common denominator (LCD) is 88.

• Step 1. Convert \(\frac{7}{8}\): multiply numerator and denominator by 11.
  \[\frac{7}{8} = \frac{7 \times 11}{8 \times 11} = \frac{77}{88}\]
• Step 2. Convert \(\frac{8}{11}\): multiply numerator and denominator by 8.
  \[\frac{8}{11} = \frac{8 \times 8}{11 \times 8} = \frac{64}{88}\]
• Step 3. Compare the numerators: 77 vs 64.
• Step 4. Since 77 is greater than 64, we know that \(\frac{7}{8} > \frac{8}{11}\).

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: \(7 \times 11 = 77\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(8 \times 8 = 64\).
• Step 3. Compare the products: \(77 > 64\), so \(\frac{7}{8} > \frac{8}{11}\).

Method 3: Decimal Comparison

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

Since 0.875 is greater than 0.727273, we confirm that \(\frac{7}{8} > \frac{8}{11}\). In percentage terms, \(\frac{7}{8}\) is 87.5% and \(\frac{8}{11}\) is 72.7273%, a difference of 14.7727 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 88, we're cutting both quantities into equal-sized pieces. Then 77 pieces vs 64 pieces is a straightforward comparison.