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Chapter 1: Problem 115

In the following exercises, simplify using the order of operations. $$ 4 \cdot 12 / 8 $$

Short Answer

Expert verified
The simplified result is 6.

Step by step solution

01

Identify the expression

The expression to simplify is \[ 4 \times 12 \/ 8 \]
02

Apply the order of operations

The order of operations (PEMDAS/BODMAS) tells us to perform multiplication and division from left to right. First, multiply 4 and 12.
03

Perform the multiplication

Calculate \[ 4 \times 12 = 48 \]
04

Perform the division

Now, divide the result by 8. \[ 48 \/ 8 = 6 \]
05

State the simplified result

The simplified result of the expression is 6.

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Key Concepts

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

PEMDAS
In mathematics, the order of operations is crucial for solving expressions correctly. One helpful acronym to remember the correct order is PEMDAS.
P stands for Parentheses, E for Exponents, M for Multiplication, D for Division, A for Addition, and S for Subtraction.
This means you should always evaluate parts of the equation inside parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). These steps ensure consistency across all calculations.
Following PEMDAS, for the expression in the exercise, you need to handle multiplication and division before any addition or subtraction.
Simplification
Simplification involves breaking down complicated expressions into easier, more manageable components.
This often means applying arithmetic operations step-by-step according to the order of operations.
For example, with the expression \[ 4 \times 12 / 8 \], simplification starts by recognizing and performing multiplication and division operations. This process helps avoid mistakes and ensures you understand the rationale behind each step.
The simplification of the given example led us first to calculate \[ 4 \times 12 = 48 \], and then perform the division \[ 48 / 8 = 6 \]. This methodical approach guarantees accurate results.
Multiplication and Division
Multiplication and division are basic arithmetic operations, but their correct application within an expression is guided by the order of operations, specifically PEMDAS.
When both operations appear, they are processed from left to right, as demonstrated in the given problem. You first multiply 4 by 12 to get 48. Then divide 48 by 8 to reach the final result, 6.
This showcases that even simple calculations can be prone to errors if the order of operations is not followed. Practicing this ensures precision in more complex problems.

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