Final answer:
To simplify the calculation 2×(473×5), we rearrange the numbers using the commutative property of multiplication, making it a straightforward multiplication of 5 by 473, and then by 2, resulting in 4730.
Step-by-step explanation:
Understanding Basic Arithmetic Rules for Simplification
To simplify the calculation 2×(473×5) using the basic rules of arithmetic, we can apply the associative property of multiplication. Instead of performing operations in the parentheses first, we can rearrange the multiplication sequence because multiplication is commutative, which means we can multiply numbers in any order and still get the same result.
So, the expression can be rewritten as:
2×(473×5) = 2×(5×473) (commutative property)
Now we can multiply 5 by 473, which gives us 2365.
Then, we multiply 2 by 2365, which results in 4730.
In summary, by simply rearranging the numbers, we arrive at an equivalent but more straightforward calculation: 2×(473×5) = 2×(5×473) = 4730.
This approach exemplifies how understanding and applying mathematical properties can streamline the calculation process, making it easier to perform complex arithmetic in our heads. By recognizing patterns and applying these properties, we can solve problems more efficiently.