Problem 11 Simplify. Show your steps. $$2... [FREE SOLUTION]

Chapter 1: Problem 11

Simplify. Show your steps. $$25+2(14-9)$$

Short Answer

Expert verified

Answer: The simplified form of the expression is 35.

Step by step solution

Evaluate the expression within the parentheses

We start by evaluating the expression inside the parentheses: $(14-9)$. To do this, subtract 9 from 14: $(14-9)=5$ Now, the expression becomes: $$25+2(5)$$

Perform the multiplication

Next, we perform the multiplication: $2\times5$. To do this, simply multiply the two numbers: $2\times5=10$ Now, the expression becomes: $$25+10$$

Perform the addition

Finally, we perform the addition: $25+10$. To do this, simply add the two numbers: $25+10=35$ So, after simplifying the expression, the result is: $$25+2(14-9)=35$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations

Understanding the order of operations is fundamental in simplifying mathematical expressions. It follows a specific sequence called PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This rule helps us determine which part of the expression to solve first.

For example, in the expression $25+2(14-9)$, we first address what's inside the parentheses鈥攖his is the 'P' in PEMDAS. After we simplify the expression within the parentheses, we continue with the remaining operations in the correct order: multiplication and then addition, as per the PEMDAS sequence.

Arithmetic Operations

Arithmetic operations are the cornerstone of most mathematical calculations, including addition, subtraction, multiplication, and division. These operations allow us to combine numbers and solve equations.

In relation to the exercise, once we complete operations within the parentheses, we move on to multiplication. It's essential to execute these operations correctly to reach the correct simplification of the expression. As shown in the exercise's solution, multiplying $2 \times 5$ correctly results in 10, which is then ready to be added to 25.

Evaluating Expressions

Evaluating expressions involves carrying out the operations within an expression to arrive at a single numerical value. This process requires a careful application of the order of operations and precise execution of arithmetic operations.

In the exercise $25+2(14-9)$, we demonstrate how to evaluate expressions by first handling what's inside the parentheses, then multiplying, and finally adding. This step-by-step approach is essential to avoid mistakes and to simplify the expression correctly to $35$, the final answer.

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91影视

Simplify. Show your steps. $$25+2(14-9)$$

Short Answer

Step by step solution

Evaluate the expression within the parentheses

Perform the multiplication

Perform the addition

Key Concepts

Order of Operations

Arithmetic Operations

Evaluating Expressions

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