Opening Parentheses, Regularities

Deepen your knowledge with an interactive video lesson on this topic in our app. Quizzes and pauses will help you better absorb the material!

In mathematics, parentheses are an essential tool that help us control and indicate the order of operations in calculating numerical expressions. They allow us to group numbers and operations so that the expression is calculated in the correct order. Understanding the use of parentheses is important in solving both simple and complex mathematical problems. If we have the expression a plus b in parentheses, and we add a plus sign in front, opening the parentheses does not change the signs inside the parentheses. Like this. However, if to the same expression we add a minus sign in front, then opening the parentheses, the signs of the numbers inside the parentheses are reversed. Like this. Let's look at this more carefully. Here is a schematic example table with a positive and negative sign before the parentheses. If there is a plus sign before the parentheses, then, by dropping the parentheses, the signs of the numbers enclosed in parentheses do not change. Like this. Conversely, If there is a minus sign before the parentheses, In this case, dropping the parentheses changes the signs of the numbers inside to the opposite. Like this. Now try to independently drop the parentheses to these expressions, and check if you understand how the signs before the parentheses affect the result. Good. Remember - multiplying two numbers with different signs (for example, positive and negative) the result is negative, but multiplying two negative numbers, the result is positive. This knowledge will also be useful in budgeting or making measurements in physics, where different signs can mean different directions or states.

Opening Parentheses: Rules and Applications in Mathematics

Understanding the role of parentheses in mathematics is crucial for solving both simple and complex mathematical problems. Parentheses help in indicating the order in which operations in numerical expressions should be performed, ensuring calculations are done correctly. This article explores the concept of opening parentheses and the rules governing this process, providing new insights, methods, and examples to deepen students' understanding.

What Happens When You Open Parentheses?

Positive Before Parentheses: If there's a plus sign before the parentheses, opening them does not change the signs of the numbers inside. This means the operation within the parentheses is performed as is.

Negative Before Parentheses: Conversely, a minus sign before the parentheses means that upon opening them, the signs of the numbers inside are reversed. This rule is vital for understanding how to manipulate expressions correctly.

Examples to Consider

Example 1: Consider the expression (3 + 4). Adding a plus sign before the parentheses, we simply get 3 + 4. However, adding a minus before the same parentheses, - (3 + 4), the expression becomes -3 - 4.

Example 2: Let's take another expression, (5 - 2). With a plus sign before it, it remains 5 - 2. But with a minus sign, it turns into -5 + 2.

Practical Application

Understanding how to open parentheses is not just a mathematical exercise. It's applicable in budget planning, measurements in physics, and anywhere differences in signs indicate different directions or states. Applying these concepts to real-world situations enhances comprehension and retention.