Is 4/5 Bigger Than 7/10?

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 5 and 10, and the least common denominator (LCD) is 10.

• Step 1. Convert \(\frac{4}{5}\): multiply numerator and denominator by 2.
  \[\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}\]
• Step 2. Keep \(\frac{7}{10}\) as it is — the denominator is already 10.
• Step 3. Compare the numerators: 8 vs 7.
• Step 4. Since 8 is greater than 7, we know that \(\frac{4}{5} > \frac{7}{10}\).

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: \(7 \times 5 = 35\).
• Step 3. Compare the products: \(40 > 35\), so \(\frac{4}{5} > \frac{7}{10}\).

Method 3: Decimal Comparison

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

Since 0.8 is greater than 0.7, we confirm that \(\frac{4}{5} > \frac{7}{10}\). In percentage terms, \(\frac{4}{5}\) is 80% and \(\frac{7}{10}\) is 70%, a difference of 10 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 10, we're cutting both quantities into equal-sized pieces. Then 8 pieces vs 7 pieces is a straightforward comparison.