Question

3.Consider the expression 8 +4×2²-2×3

(a) What is the value of the expression? (solve it) SHOW YOUR WORK!
(b) Where could you put parentheses so the value (answer) would be 42?
Rewrite the expression with the parentheses and show the value.
(rewrite and solve) SHOW YOUR WORK!
(C) Why is order of operation important? Answer in your own words!

Answer 1

The order of operations is important in mathematics to ensure consistent calculations. To evaluate the expression 8 + 4×2² - 2×3, we follow the order of operations: PEMDAS. The value of the expression is 18. Parentheses can be added to make the expression value 42.

Step-by-step explanation:

To solve the expression 8 + 4×2² - 2×3, we need to follow the order of operations, which is a set of rules that tells us which operations to perform first. The acronym PEMDAS can help us remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

1. The first step is to simplify the exponents. Since 2² means 2 raised to the power of 2, we have 8 + 4×4 - 2×3.
2. Next, we perform multiplication and division from left to right. 4×4 is 16, so the expression becomes 8 + 16 - 2×3.
3. Finally, we perform addition and subtraction from left to right. The final calculation is 8 + 16 - 6, which equals 18.

(b) To make the expression value 42, we can put parentheses around 8 + 4×2². By doing this, the expression becomes (8 + 4)×2² - 2×3.

The value of the expression with the added parentheses is (12)×2² - 2×3. Simplifying further, we have 12×4 - 6, which equals 48 - 6 and gives us a value of 42.

(c) The order of operations is important because it provides a set of rules that ensure consistent and unambiguous calculations. Without these rules, different people may interpret an expression differently and arrive at different answers.

Learn more about Order of operations in mathematics