Final answer:
The best use of the associative property to simplify the expression 2/7 - 17 * 6 - 5/7 * 1 is represented by option 1, which correctly groups multiplication within parentheses, allowing for correct order of operations without altering the expression.
Step-by-step explanation:
The question asks us to use the associative property of multiplication and addition to simplify the given expression. The associative property allows us to regroup numbers without changing the result. Taking a look at the provided options, we need to first identify which option correctly applies the associative property to the given expression (2/7 - 17 * 6 - 5/7 * 1).
Option 1) 2/7 - (17 * 6) - (5/7 * 1) is the correct application of the associative property. Here, multiplication is performed first within the parentheses, as indicated by the order of operations (PEMDAS/BODMAS). The subtraction operations are intact as in the original expression.
Option 2) (2/7 - 17) * (6 - 5/7) * 1 changes the expression significantly by grouping the subtraction, which does not simplify the original expression according to the associative property.
Option 3) 2/7 - (17 * 6 - 5/7 * 1) uses the associative property incorrectly by grouping the subtraction and multiplication together which alters the intended order of operations.
Option 4) (2/7 - 17 * 6) - (5/7 * 1) also incorrectly uses the associative property by grouping subtraction with multiplication.
Therefore, option 1 is the best representation of the associative property to simplify the expression without altering the meaning.