Step-by-step working
- Multiply the numerators and the denominators: (2 × 2) / (3 × 3) = 4/9.
2/3 times 2/3 as an area
Multiplying 2/3 by 2/3 is the same as squaring 2/3: (2/3)² = 2² ÷ 3² = 4/9. Picture a square cut into 3 equal columns and 3 equal rows, which makes 9 small squares. Shade 2 of the 3 columns and 2 of the 3 rows: the 4 small squares where the shading overlaps are 4 of the 9, so 4/9 of the whole square.
The answer, about 0.444, is smaller than 2/3 (about 0.667) because you are taking two thirds of an amount that is already less than 1. Any fraction between 0 and 1 gets smaller when you multiply it by itself. A common mistake is to add instead: 2/3 + 2/3 = 4/3, which is three times the correct answer of 4/9.