Problem 35 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ [(7 \cdot 4)+3]+15 $$

Step-by-Step Solution

Answer

The evaluated result of the expression \( [(7 \cdot 4)+3]+15 \) is 46.

Step 1: Solving the Parentheses

Starting from the inner part of the parentheses, calculate \(7 \cdot 4\), which equals 28. Then add 3 to get 31. So, the new expression becomes: \[(31)+15\]

Step 2: Solving the Addition

Now that we only have one operation left, addition, we add up 31 and 15 to get 46.

Step 3: Final Result

From the result of the addition, the solution to the expression \( [(7 \cdot 4)+3]+15 \) is 46.

Key Concepts

Order of Operations

When evaluating mathematical expressions, it’s crucial to follow the order of operations. This ensures that you arrive at the correct answer. Think of it as a set of rules guiding you through the problem. The acronym PEMDAS will help you remember the correct order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Beginning with parentheses means you solve anything inside brackets first. Inside the brackets of \( [(7 \cdot 4)+3]+15 \), you first calculate \(7 \cdot 4\). This ensures we handle operations inside out. As shown, the parentheses simplify the complexity of expressions, letting you tackle them step-by-step.

Basic Arithmetic

Basic arithmetic involves performing operations such as addition, subtraction, multiplication, and division. In evaluating the expression \( [(7 \cdot 4)+3]+15 \), you apply multiplication first because of the parentheses, calculating \(7 \cdot 4 = 28\). Next, the operation involves adding the 3, yielding 31. Then, outside the parentheses, you sum up 31 with 15, giving a final result of 46. These simple operations form the foundation of many mathematical concepts, making it vital to master them thoroughly. Practicing these calculations helps build your confidence in solving more complex expressions.

Mathematical Expressions

Mathematical expressions are combinations of numbers, operators, and sometimes variables, structured to convey a specific calculation task. In the expression \( [(7 \cdot 4)+3]+15 \), you see a straightforward sequence of operations. Understanding how to read and deconstruct these expressions is critical. Notice how brackets help clarify the order in which you carry out operations. By breaking down each part: multiplication inside the brackets first, followed by addition, then the external addition, you simplify the tasks into manageable steps. Knowing this structure is key to making sense of any expression you encounter. It's essentially like solving a puzzle, where each piece must fit perfectly to reveal the correct solution.