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Chapter 2: Problem 441

In the following exercises, simplify, using the order of operations. $$ (8+1) \cdot 4 $$

Short Answer

Expert verified
36

Step by step solution

01

- Calculate Inside the Parentheses

First, perform the operation inside the parentheses: \(8 + 1\). Adding these together, we get: \(8 + 1 = 9\).
02

- Multiply by 4

Next, take the result from Step 1 and multiply by 4. So, \(9 \times 4 = 36\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions involves performing operations to make the expression easier to understand or solve. This often requires us to follow the order of operations, also known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

In the provided example, the expression \( (8 + 1) \cdot 4 \) needs simplification. Here鈥檚 how you simplify it:
  • Look for any arithmetic operation that can be simplified, starting with the innermost parentheses.
  • Perform the operations in the correct order according to PEMDAS.
In this example, after handling the parentheses, we are left with an easier expression to solve. Following these steps ensures consistency and correctness.
Parentheses
Parentheses are used in mathematics to indicate which operations should be performed first in an expression. They take the highest priority in the order of operations. When you see parentheses, always perform the calculations inside them before dealing with any operations outside.

In the expression \( (8+1) \cdot 4 \), the operation inside the parentheses \( (8+1) \) is done first. Solving this, we get 9.

Parentheses help to clarify the structure of expressions and ensure that everyone solves the expression in the same way. They make the complex calculations manageable and avoid ambiguity.
  • Always solve inside the parentheses first.
  • Work your way from the innermost set of parentheses outwards if there are multiple sets.
Multiplication
Once any parentheses have been dealt with, the next step is to perform any multiplication or division, working from left to right. Multiplication is a fundamental arithmetic operation that combines groups of equal size.

In our example, after solving the parentheses \( (8+1) = 9 \), we multiply 9 by 4. So, \( 9 \times 4 = 36 \).

This step is essential because failing to follow the correct order can lead to incorrect results. Always remember that multiplication and division should be handled before addition and subtraction when following PEMDAS.
  • Perform any multiplication or division after dealing with parentheses.
  • Work from left to right for these operations.

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