Final answer:
To override the order of operations in arithmetic expressions, you can include parentheses. Parentheses change the sequence of operations, ensuring that the operations within them are performed first, and can significantly alter the results of calculations.
Step-by-step explanation:
You can include parentheses to override the order of operations when solving arithmetic expressions. The order of operations, known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is a fundamental concept in mathematics that dictates the order in which operations should be performed to ensure that everyone calculates the same result for a given expression.
By using parentheses, we can alter this sequence. For example, in the expression 2 + 3 × 4, the multiplication is performed first, resulting in 2 + 12, which equals 14. However, if we want the addition to occur before the multiplication, we can write the expression as (2 + 3) × 4, which equals 5 × 4 and results in 20. The presence of the parentheses changes the result because it directs us to add 2 and 3 before multiplying by 4.
It's important to remember when performing arithmetic operations that you cannot add or subtract quantities with different dimensions, just as you can't add apples and oranges. Additionally, multiplication or division must apply to every term on either side of an equation, which can be achieved by enclosing terms in parentheses before performing these operations.