Is 7/11 Bigger Than 5/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 11 and 12, and the least common denominator (LCD) is 132.

• Step 1. Convert \(\frac{7}{11}\): multiply numerator and denominator by 12.
  \[\frac{7}{11} = \frac{7 \times 12}{11 \times 12} = \frac{84}{132}\]
• Step 2. Convert \(\frac{5}{12}\): multiply numerator and denominator by 11.
  \[\frac{5}{12} = \frac{5 \times 11}{12 \times 11} = \frac{55}{132}\]
• Step 3. Compare the numerators: 84 vs 55.
• Step 4. Since 84 is greater than 55, we know that \(\frac{7}{11} > \frac{5}{12}\).

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: \(7 \times 12 = 84\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(5 \times 11 = 55\).
• Step 3. Compare the products: \(84 > 55\), so \(\frac{7}{11} > \frac{5}{12}\).

Method 3: Decimal Comparison

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

Since 0.636364 is greater than 0.416667, we confirm that \(\frac{7}{11} > \frac{5}{12}\). In percentage terms, \(\frac{7}{11}\) is 63.6364% and \(\frac{5}{12}\) is 41.6667%, a difference of 21.9697 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 132, we're cutting both quantities into equal-sized pieces. Then 84 pieces vs 55 pieces is a straightforward comparison.