Is 3/4 Bigger Than 2/7?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 4 and 7, and the least common denominator (LCD) is 28.

• Step 1. Convert \(\frac{3}{4}\): multiply numerator and denominator by 7.
  \[\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}\]
• Step 2. Convert \(\frac{2}{7}\): multiply numerator and denominator by 4.
  \[\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28}\]
• Step 3. Compare the numerators: 21 vs 8.
• Step 4. Since 21 is greater than 8, we know that \(\frac{3}{4} > \frac{2}{7}\).

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: \(3 \times 7 = 21\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(2 \times 4 = 8\).
• Step 3. Compare the products: \(21 > 8\), so \(\frac{3}{4} > \frac{2}{7}\).

Method 3: Decimal Comparison

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

Since 0.75 is greater than 0.285714, we confirm that \(\frac{3}{4} > \frac{2}{7}\). In percentage terms, \(\frac{3}{4}\) is 75% and \(\frac{2}{7}\) is 28.5714%, a difference of 46.4286 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 28, we're cutting both quantities into equal-sized pieces. Then 21 pieces vs 8 pieces is a straightforward comparison.