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Chapter 15: Problem 42

Simplify. $$ 3-11+2 \cdot 4 $$

Short Answer

Expert verified
The simplified expression is 0.

Step by step solution

01

Identify the Order of Operations

The order of operations follows the PEMDAS rule: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
02

Perform Multiplication

According to PEMDAS, multiplication should be performed before addition and subtraction. Calculate the product of 2 and 4.\( 2 \times 4 = 8 \)
03

Rewrite the Expression

Now rewrite the expression with the multiplication result:3 - 11 + 8
04

Perform Addition and Subtraction

Evaluate the expression from left to right, performing addition and subtraction as they appear.\( 3 - 11 = -8 \)\( -8 + 8 = 0 \)

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Key Concepts

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

PEMDAS
To solve any mathematical expression correctly, we must follow the order of operations, often referred to by the acronym PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It's like a set of rules that tell us which calculations to perform first. Without following PEMDAS, we'd all get different results for the same expression! For example, in the expression given: 3 - 11 + 2 * 4, we must follow these specific steps to avoid mistakes.
Multiplication
According to PEMDAS, multiplication comes before addition and subtraction. This means we need to handle all multiplication in the expression before doing any adding or subtracting. In the example 3 - 11 + 2 * 4, multiplication is the first operation we perform. So we calculate: 2 * 4 = 8. Now the expression looks like this: 3 - 11 + 8. Only after dealing with multiplication can we proceed to addition and subtraction.
Addition and Subtraction
Once multiplication has been completed, we move on to addition and subtraction. These operations are performed from left to right. Hence for the expression 3 - 11 + 8, we start with 3 - 11. First, calculate: 3 - 11 = -8. Then, we add the result to 8, so we get: -8 + 8 = 0. Voila! The final result for the expression 3 - 11 + 2 * 4 is 0. By following the order of operations (PEMDAS) and handling multiplication before addition or subtraction, we ensure our answer is correct.

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Most popular questions from this chapter

The sum of two numbers is \(89 .\) One number is 3 more than the other. Find the numbers.

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