Is 5/8 Bigger Than 7/12?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 8 and 12, and the least common denominator (LCD) is 24.

• Step 1. Convert \(\frac{5}{8}\): multiply numerator and denominator by 3.
  \[\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}\]
• Step 2. Convert \(\frac{7}{12}\): multiply numerator and denominator by 2.
  \[\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}\]
• Step 3. Compare the numerators: 15 vs 14.
• Step 4. Since 15 is greater than 14, we know that \(\frac{5}{8} > \frac{7}{12}\).

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: \(5 \times 12 = 60\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 8 = 56\).
• Step 3. Compare the products: \(60 > 56\), so \(\frac{5}{8} > \frac{7}{12}\).

Method 3: Decimal Comparison

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

Since 0.625 is greater than 0.583333, we confirm that \(\frac{5}{8} > \frac{7}{12}\). In percentage terms, \(\frac{5}{8}\) is 62.5% and \(\frac{7}{12}\) is 58.3333%, a difference of 4.1667 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 15 pieces vs 14 pieces is a straightforward comparison.