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Chapter 1: Problem 32

Evaluate each expression. $$-12 / 4 \cdot 3$$

Short Answer

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Step by step solution

01

Divide the numbers

First, perform the division from left to right. Evaluate \(-12 \div 4 \), which equals \[ -3 \].
02

Multiply the result

Next, multiply the result from Step 1 by 3. So, \( -3 \cdot 3 \), which equals \[ -9 \].

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Key Concepts

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

Division
Division is one of the fundamental arithmetic operations. It essentially means splitting a number into equal parts. In this example, we start by dividing \(-12\) by \(4\).
This means we need to figure out how many times \(4\) fits into \(-12\). When doing this calculation, it's important to remember the signs:

  • Dividing a negative number by a positive number results in a negative result.
So, \(-12 \div 4 = -3\).
After performing this division, we move on to the next step, where we use this result for further calculations.
Multiplication
Multiplication is another essential arithmetic operation. It is essentially repeated addition. For example, \(4 \times 3\) means adding \(4\) to itself \(3\) times.
In our example, we now need to multiply the result from the division step by \(3\).
  • Multiply \(-3\) (the result of \(-12 \div 4\)) by \(3\), which gives \(-3 \times 3 = -9\).
Just like division, it's crucial to watch the signs.
Since both numbers being multiplied have different signs (one negative and one positive), the result will be negative.
Order of Operations
The order of operations is a rule used to clarify which procedures should be performed first in a given mathematical expression.
The acronym PEMDAS helps remember this order:
  • \textbf{P}: Parentheses
  • \textbf{E}: Exponents
  • \textbf{MD}: Multiplication and Division (from left to right)
  • \textbf{AS}: Addition and Substraction (from left to right)

According to these rules, we first perform any operations inside parentheses, followed by exponents. Then, we handle multiplication and division from left to right.
In our exercise, even though it includes both division and multiplication, we follow the left-to-right rule. First, we divide \(-12\) by \(4\), and then we multiply the result by \(3\), reflecting the proper use of the order of operations.

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