82×5

82×5 is a basic arithmetic expression that denotes the product of the integers 82 and 5. The computed result is 410.

Calculation can be shown in multiple straightforward ways. Direct multiplication yields 82×5 = 410. A common mental-math approach is to use distributive property: 82×5 = (80+2)×5 = 80×5 + 2×5 = 400 + 10 = 410. Another efficient method is to multiply by 10 and then halve: 82×10 = 820, and 820÷2 = 410. These methods exemplify place-value understanding and the interplay between operations such as addition, multiplication, and division.

Properties and context. The equality 82×5 = 5×82 holds due to commutativity of multiplication. The prime factorization of the factors shows 82 = 2×41 and 5 is prime, so the product factors as 2×5×41 = 410. The greatest common divisor of 82 and 5 is 1, so the numbers are coprime.

Representations and usage. In decimal notation, the product is written as 410. In other bases, the same product would have a different digit representation. As a simple example, 82×5 is frequently used in teaching basic multiplication, mental math strategies, and demonstrations of the distributive and commutative properties in introductory arithmetic.

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