Is 3/4 Bigger Than 7/8?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 4 and 8, and the least common denominator (LCD) is 8.

• Step 1. Convert \(\frac{3}{4}\): multiply numerator and denominator by 2.
  \[\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}\]
• Step 2. Keep \(\frac{7}{8}\) as it is — the denominator is already 8.
• Step 3. Compare the numerators: 6 vs 7.
• Step 4. Since 6 is less than 7, we know that \(\frac{3}{4} < \frac{7}{8}\).

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: \(3 \times 8 = 24\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 4 = 28\).
• Step 3. Compare the products: \(24 < 28\), so \(\frac{3}{4} < \frac{7}{8}\).

Method 3: Decimal Comparison

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

Since 0.75 is less than 0.875, we confirm that \(\frac{3}{4} < \frac{7}{8}\). In percentage terms, \(\frac{3}{4}\) is 75% and \(\frac{7}{8}\) is 87.5%, a difference of 12.5 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 8, we're cutting both quantities into equal-sized pieces. Then 6 pieces vs 7 pieces is a straightforward comparison.