What is the purpose of using parentheses in mathematical expressions?

The purpose of using parentheses in mathematical expressions is to indicate the order of operations or to group certain parts of the expression together. Parentheses help clarify the intended meaning of the expression and ensure that the mathematical operations are performed correctly.

One of the main uses of parentheses is to indicate the order of operations in an expression. In mathematics, there are specific rules that dictate the sequence in which different operations should be performed. These rules are commonly known as the "order of operations" or "PEMDAS" (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Parentheses are used to override the default order of operations and indicate that the operations within the parentheses should be performed first.

For example, consider the expression 2 + 3 * 4. According to the order of operations, multiplication should be performed before addition. However, if we want to change the order and perform the addition first, we can use parentheses to indicate this: (2 + 3) * 4. In this case, the operations within the parentheses are performed first, resulting in 5, and then the multiplication is carried out, resulting in 20.

Parentheses are also used to group certain parts of an expression together. This can be helpful when dealing with complex expressions or when we want to emphasize a specific part of the expression. By enclosing a group of numbers, variables, or operations within parentheses, we can treat them as a single entity and perform operations on them as a whole.

For example, consider the expression 2 * (3 + 4). The parentheses here indicate that the addition operation should be performed first, resulting in 7. Then, the multiplication is carried out, resulting in 14. Without the parentheses, the expression would be evaluated as 2 * 3 + 4, which would yield a different result of 10.

In summary, the purpose of using parentheses in mathematical expressions is to indicate the order of operations and to group certain parts of the expression together. They help clarify the intended meaning of the expression and ensure that the mathematical operations are performed correctly.