Is 7/8 Bigger Than 3/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 8 and 10, and the least common denominator (LCD) is 40.

• Step 1. Convert \(\frac{7}{8}\): multiply numerator and denominator by 5.
  \[\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}\]
• Step 2. Convert \(\frac{3}{10}\): multiply numerator and denominator by 4.
  \[\frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40}\]
• Step 3. Compare the numerators: 35 vs 12.
• Step 4. Since 35 is greater than 12, we know that \(\frac{7}{8} > \frac{3}{10}\).

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: \(7 \times 10 = 70\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(3 \times 8 = 24\).
• Step 3. Compare the products: \(70 > 24\), so \(\frac{7}{8} > \frac{3}{10}\).

Method 3: Decimal Comparison

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

Since 0.875 is greater than 0.3, we confirm that \(\frac{7}{8} > \frac{3}{10}\). In percentage terms, \(\frac{7}{8}\) is 87.5% and \(\frac{3}{10}\) is 30%, a difference of 57.5 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 40, we're cutting both quantities into equal-sized pieces. Then 35 pieces vs 12 pieces is a straightforward comparison.