Is 3/4 Bigger Than 3/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 4 and 10, and the least common denominator (LCD) is 20.

• Step 1. Convert \(\frac{3}{4}\): multiply numerator and denominator by 5.
  \[\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\]
• Step 2. Convert \(\frac{3}{10}\): multiply numerator and denominator by 2.
  \[\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}\]
• Step 3. Compare the numerators: 15 vs 6.
• Step 4. Since 15 is greater than 6, we know that \(\frac{3}{4} > \frac{3}{10}\).

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: \(3 \times 10 = 30\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(3 \times 4 = 12\).
• Step 3. Compare the products: \(30 > 12\), so \(\frac{3}{4} > \frac{3}{10}\).

Method 3: Decimal Comparison

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

Since 0.75 is greater than 0.3, we confirm that \(\frac{3}{4} > \frac{3}{10}\). In percentage terms, \(\frac{3}{4}\) is 75% and \(\frac{3}{10}\) is 30%, a difference of 45 percentage points.

Why Does This Work?

When two fractions have the same numerator, you have the same number of pieces — but the pieces are different sizes. A smaller denominator means each piece is larger. Since 10ths are larger pieces than 4ths, \(\frac{3}{4}\) is the bigger fraction even though both have 3 in the numerator.