/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 Evaluate each expression. $$4-... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 29

Evaluate each expression. $$4-6 \cdot 2$$

Short Answer

Expert verified
-8

Step by step solution

01

Understand the Order of Operations

To solve the expression, we need to use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
02

Identify Operations

In the expression \(4-6 \times 2\), we have subtraction and multiplication. According to PEMDAS, we handle multiplication before subtraction.
03

Perform Multiplication

Calculate the multiplication part of the expression first: \(6 \times 2 = 12\).
04

Substitute Back

Replace the multiplication part in the original expression with the result: \(4-12\).
05

Perform Subtraction

Now, perform the subtraction: \(4-12=-8\).

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Key Concepts

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

PEMDAS
When solving mathematical expressions, it's crucial to follow the order of operations. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It helps you know which operations to perform first and ensures you get the correct answer.
For example, if you have the expression \(4-6 \times 2\), you need to follow PEMDAS. This means you'll handle multiplication before doing any addition or subtraction. Ignoring PEMDAS can lead to incorrect answers. Always start by identifying the different operations in your expression and then proceed according to PEMDAS.
multiplication
In this problem \(4 - 6 \times 2\), multiplication plays a key role. According to PEMDAS, you should perform multiplication before subtraction.
First, look at the multiplication part of your expression: '6 \times 2'. Calculate this part to get 12. Now, substitute this value back into the original expression. This step transforms your original expression \(4 - 6 \times 2\) into \(4 - 12\).
Understanding how to handle multiplication within the context of PEMDAS is fundamental. It helps you simplify expressions correctly and prevents mistakes.
subtraction
Subtraction is another core concept in this problem. After performing the multiplication, we need to handle the remaining subtraction.
Once we substituted the multiplication result, our expression became \(4 - 12\). Now, perform the subtraction: 4 minus 12 equals \(-8\).
This final step demonstrates how subtraction follows after you have handled other operations according to PEMDAS. By dealing with each step systematically, you ensure accuracy in your calculations.

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