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CEMC Fermat, 2024 Difficulty 1.0 Junior Find the answer Canada
The value of 3 ( 5 3 − 1 3 ) 3\left(\frac 53-\frac 13\right) 3 ( 3 5 − 3 1 )
Pick one
A 1 1 1 B 2 2 2 C 3 3 3 D 4 4 4 E 6 6 6
Solution Calculating, 3 ( 5 3 − 1 3 ) = 3 ⋅ 5 3 − 3 ⋅ 1 3 = 5 − 1 = 4 3 \left(\frac{5}{3}-\frac{1}{3}\right) = 3 \cdot \frac{5}{3} - 3 \cdot \frac{1}{3} = 5 - 1 = 4 3 ( 3 5 − 3 1 ) = 3 ⋅ 3 5 − 3 ⋅ 3 1 = 5 − 1 = 4
Alternatively, 3 ( 5 3 − 1 3 ) = 3 ⋅ 4 3 = 4 3 \left(\frac{5}{3}-\frac{1}{3}\right) = 3 \cdot \frac{4}{3} = 4 3 ( 3 5 − 3 1 ) = 3 ⋅ 3 4 = 4
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