Is 5/6 Bigger Than 7/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 6 and 10, and the least common denominator (LCD) is 30.

• Step 1. Convert \(\frac{5}{6}\): multiply numerator and denominator by 5.
  \[\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\]
• Step 2. Convert \(\frac{7}{10}\): multiply numerator and denominator by 3.
  \[\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}\]
• Step 3. Compare the numerators: 25 vs 21.
• Step 4. Since 25 is greater than 21, we know that \(\frac{5}{6} > \frac{7}{10}\).

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: \(5 \times 10 = 50\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 6 = 42\).
• Step 3. Compare the products: \(50 > 42\), so \(\frac{5}{6} > \frac{7}{10}\).

Method 3: Decimal Comparison

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

Since 0.833333 is greater than 0.7, we confirm that \(\frac{5}{6} > \frac{7}{10}\). In percentage terms, \(\frac{5}{6}\) is 83.3333% and \(\frac{7}{10}\) is 70%, a difference of 13.3333 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 25 pieces vs 21 pieces is a straightforward comparison.