Question

Explain why grouping symbols can change the value of a numerical expression. Then insert grouping symbols to show four different values for the following expression. 80:8x5+8

Answer 1

Grouping symbols modify the order of operations in a numerical expression, thereby altering the final value. By changing the groupings in the expression 80:8x5+8, we can obtain four different values: 58, 0.769, 1.667, and 130.

Step-by-step explanation:

Grouping symbols in mathematics, like parentheses, brackets, or braces, can change the order of operations in a numerical expression, thus potentially changing the final value of that expression. This is because the operations within the grouping symbols are performed first according to the mathematical conventions of order of operations (PEMDAS/BODMAS).

Let's take the expression 80:8x5+8 and insert grouping symbols to show four different values:

1. (80:8)x5+8 = 10x5+8 = 50+8 = 58
2. 80:(8x(5+8)) = 80:(8x13) = 80:104 = 0.769 (approx)
3. 80:((8x5)+8) = 80:(40+8) = 80:48 = 1.667 (approx)
4. (80:8)x(5+8) = (10)x(13) = 130

The associative and distributive properties allow us to regroup and change the order of multiplication and division, leading to different outcomes based on the positioning of the grouping symbols.