Is 3/10 Bigger Than 7/10?

Method 1: Common Denominators

These fractions already share the same denominator: 10. We just need to compare the numerators.

• Step 1. Both fractions already have the same denominator: 10.
• Step 2. Compare the numerators: 3 vs 7.
• Step 3. Since 3 is less than 7, we know that \(\frac{3}{10} < \frac{7}{10}\).

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: \(3 \times 10 = 30\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 10 = 70\).
• Step 3. Compare the products: \(30 < 70\), so \(\frac{3}{10} < \frac{7}{10}\).

Method 3: Decimal Comparison

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

Since 0.3 is less than 0.7, we confirm that \(\frac{3}{10} < \frac{7}{10}\). In percentage terms, \(\frac{3}{10}\) is 30% and \(\frac{7}{10}\) is 70%, a difference of 40 percentage points.

Why Does This Work?

When two fractions share the same denominator, the pieces are the same size. A fraction with more pieces (a larger numerator) is simply a larger amount. Since 7 pieces is more than 3 pieces of the same size, \(\frac{7}{10}\) is the larger fraction.