Is 4/7 Bigger Than 7/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 7 and 10, and the least common denominator (LCD) is 70.

• Step 1. Convert \(\frac{4}{7}\): multiply numerator and denominator by 10.
  \[\frac{4}{7} = \frac{4 \times 10}{7 \times 10} = \frac{40}{70}\]
• Step 2. Convert \(\frac{7}{10}\): multiply numerator and denominator by 7.
  \[\frac{7}{10} = \frac{7 \times 7}{10 \times 7} = \frac{49}{70}\]
• Step 3. Compare the numerators: 40 vs 49.
• Step 4. Since 40 is less than 49, we know that \(\frac{4}{7} < \frac{7}{10}\).

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: \(4 \times 10 = 40\).
• Step 2. Multiply the numerator of the second fraction by the denominator of the first: \(7 \times 7 = 49\).
• Step 3. Compare the products: \(40 < 49\), so \(\frac{4}{7} < \frac{7}{10}\).

Method 3: Decimal Comparison

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

Since 0.571429 is less than 0.7, we confirm that \(\frac{4}{7} < \frac{7}{10}\). In percentage terms, \(\frac{4}{7}\) is 57.1429% and \(\frac{7}{10}\) is 70%, a difference of 12.8571 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 70, we're cutting both quantities into equal-sized pieces. Then 40 pieces vs 49 pieces is a straightforward comparison.