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Chapter 0: Problem 57

Simplify each expression. $$ 12+3 \cdot 4 $$

Short Answer

Expert verified
24

Step by step solution

01

Identify the operations

Look at the expression and identify the operations to be performed. Here we have addition and multiplication: \(12 + 3 \cdot 4\)
02

Recall the order of operations

The order of operations (PEMDAS/BODMAS) tells us to perform multiplication before addition. So, we need to first solve the multiplication part of the expression.
03

Perform the multiplication

Multiply \(3\) by \(4\): \(3 \cdot 4 = 12\)
04

Perform the addition

Now add the result of the multiplication to \(12\): \(12 + 12 = 24\)

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Key Concepts

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

PEMDAS: The Order of Operations
When faced with an algebraic expression, knowing the order in which to perform operations is crucial. The acronym PEMDAS helps us remember this order: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Remember, multiplication and division are performed from left to right, and so are addition and subtraction.

In the exercise, we use PEMDAS to determine that we must first perform multiplication before addition. This ensures that we simplify the expression correctly. Without PEMDAS, you might have added first, which would give the wrong result.
Understanding Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operations. In our exercise, the expression is \({12+3 \times 4}\). Although this example does not include variables, it still follows the same principles.

When working with algebraic expressions, always look for the operations included. Highlight them if needed. In the given expression, we have addition and multiplication. Identifying these helps us apply the order of operations correctly.

Simplifying expressions step by step makes them more manageable. It also reduces the chance of mistakes.
Breaking Down Multiplication and Addition
Let's break down the exercise to understand the importance of multiplication and addition.

Step 1: Identify the operations: In \(12 + 3 \times 4\), the operations are addition and multiplication.
Step 2: Apply PEMDAS: Perform multiplication before addition. First, multiply \(3\) by \(4\), which gives \(12\).
Step 3: Perform the addition: After the multiplication, add the result to \(12\). That means \(12 + 12 = 24\).

Recognizing and performing operations in the correct order ensures that you always get the right answer. Always check your steps!

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Most popular questions from this chapter

Simplify each inequality if needed. Then determine whether the statement is true or false. $$ 2 \cdot 5 \geq 4+6 $$

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