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Parentheses are crucial in math because they help us organize and prioritize mathematical operations. They are used to group numbers and operations, telling us what to calculate first.

In the expression \(2(5+8)\), the parentheses around \(5+8\) indicate that we should perform the addition before any other operations. This is part of the order of operations rule, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Because of the parentheses, we first calculate \(5+8\), which equals 13, before moving on to other parts of the equation. The parentheses ensure that every element is computed correctly, maintaining the integrity of the mathematical process.

Multiplication is a basic arithmetic operation that involves combining groups of equal sizes. In our exercise, multiplication is indicated by the number outside the parenthesis, implying it should be multiplied with the sum inside.

When we encounter \(2(5+8)\), after solving inside the parentheses, we multiply 2 by our result (13). Multication here helps scale the value of the sum within the parentheses.

This step is straightforward in process:

• The parenthesis was calculated to 13, so the expression becomes \(2 \, \times \, 13\).
• Multiplying these gives the final answer, \(26\).

Multiplication follows the associative property, which means how we group numbers doesn’t change their product. This consistency is an essential aspect of arithmetic logic.

Arithmetic is the foundation of mathematics, involving basic operations like addition, subtraction, multiplication, and division. In this problem, we focus on both addition and multiplication.

The order of operations tells us that addition (inside the parentheses) comes before multiplication. This priority ensures accurate calculations every time.

Let's break it down:

• First, perform the addition inside the parentheses: \(5+8\) to get 13.
• Then, multiply 13 by 2 to arrive at the solution: 26.

Understanding these basic operations and their interactions is crucial, as it builds the groundwork for more complex math. Remember PEMDAS, and you'll always tackle math problems correctly!