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Chapter 2: Problem 13

Simplify using the order of operations. $$5+2(3-5)$$

Short Answer

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Step by step solution

01

Identify the Expression

The given expression is: \[ 5 + 2(3 - 5) \]
02

Perform Operations Inside Parentheses

First, solve the operation inside the parentheses: \[ 3 - 5 = -2 \]Now the expression is: \[ 5 + 2(-2) \]
03

Multiply

Next, perform the multiplication: \[ 2(-2) = -4 \]So the expression now is: \[ 5 + (-4) \]
04

Addition/Subtraction

Finally, subtract to simplify the expression: \[ 5 - 4 = 1 \]

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Key Concepts

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

Simplify Expressions
When faced with mathematical expressions, simplifying them helps to make sense of their value. The process involves breaking down complex expressions into simpler forms using mathematical rules. For example, consider the expression: \[ 5 + 2(3 - 5) \]. Simplification involves performing operations in a specified order to derive a single value. It is important to follow the rules of arithmetic operations to navigate through the expression correctly. This process helps in understanding the core value or solution the expression represents.
Parentheses
Parentheses, often represented as \( () \), are used in mathematics to group parts of expressions. They indicate that the operations within them should be performed first before addressing the rest of the expression. Following the order of operations without handling parentheses properly can lead to incorrect results. Consider the example: \( 5 + 2(3 - 5) \). Here, solving \( 3 - 5 \) first is crucial before multiplying by 2. This ensures accuracy:
  • First, calculate: \[ 3 - 5 = -2 \].
  • Then, the expression becomes: \[ 5 + 2(-2) \].
  • Next, multiply: \[ 2(-2) = -4 \].
  • Finally, add: \[ 5 + (-4) = 1 \].
Basic Arithmetic Operations
Basic arithmetic operations are fundamental to solving any mathematical expression. These operations include addition, subtraction, multiplication, and division. Understanding these basics is essential when simplifying expressions. For instance, in the expression \( 5 + 2(3 - 5) \), we utilize:
  • Subtraction: \( 3 - 5 = -2 \).
  • Multiplication: \( 2(-2) = -4 \).
  • Addition/Subtraction: \( 5 + (-4) = 1 \).
These steps reflect the importance of being comfortable with basic arithmetic operations in order to simplify expressions correctly. Remember, performing each arithmetic operation in their prescribed order ensures the correctness of the final result.

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Most popular questions from this chapter

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