By how much is 60% of 70 greater than \(\frac{1}{5}\) of 55?

Concept

To find "x% of a number A", convert the percentage to a fraction of 100 and multiply: x% of A = (x ÷ 100) × A. To find "a fraction of a number B", multiply the fraction by that number: (n/d) of B = (n/d) × B. The phrase "by how much is P greater than Q" asks for the difference P − Q, obtained after each value is computed independently in its own right.

Application

1. Compute 60% of 70: (60 ÷ 100) × 70 = 42.

2. Compute 1/5 of 55: (1 ÷ 5) × 55 = 11.

3. Find the difference: 42 − 11 = 31.

Cross-check

Cross-check using an alternate route: 60% equals the fraction 3/5, so 3/5 × 70 = 42, matching the first computation; and 55 ÷ 5 = 11, matching the second. With both component values independently confirmed, the difference 42 − 11 = 31 stands verified.

Hence, 60% of 70 exceeds 1/5 of 55 by 31.