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Chapter 1: Problem 39

Translate to an algebraic expression. The difference of \(m\) and \(n\)

Short Answer

Expert verified
\( m - n \)

Step by step solution

01

Understanding 'Difference'

The term 'difference' in mathematics refers to the result of subtracting one value from another.
02

Identify the Variable Terms

In this problem, the terms involved are represented by the variables 'm' and 'n'.
03

Set Up the Subtraction

To express the difference between two variables, write them as a subtraction expression: 'm' minus 'n'.
04

Write the Algebraic Expression

Combine the variables using a subtraction operation: \( m - n \). This is the algebraic expression for the given phrase.

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Key Concepts

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

Understanding the Term 'Difference'
The term 'difference' plays a key role when dealing with algebraic expressions. In mathematics, 'difference' simply means the result of subtracting one number or variable from another. For instance, if you have two numbers like 7 and 3, the difference is what you get when you subtract 3 from 7, which is 4. This same principle applies to variables. Understanding this concept helps you grasp more complex algebraic problems.

When you're asked to find the difference between two variables, think of it as performing a subtraction operation between those variables.
'Subtraction' in Algebraic Expressions
Subtraction is a fundamental operation in algebra. When you see words like 'difference' in a problem, it often means you'll be using subtraction.

Here's a simple breakdown to help:
  • Subtraction takes one quantity away from another.
  • In algebra, these quantities can be numbers, variables, or even more complex expressions.
  • An algebraic expression for the subtraction of two variables, like 'm' and 'n', is written as \( m - n \).

For example, if the problem states, 'the difference of \( x \) and \( y \)', you would set this up as \( x - y \). Always remember to keep the order as specified in the problem. Changing the order can result in a completely different answer.
Identifying and Working with 'Variable Terms'
In algebra, variable terms are symbols used to represent numbers. Common variables include letters like \( m \), \( n \), \( x \), and \( y \). In our problem, we are working with 'm' and 'n'.

Once you know the terms, the next step is to set up the subtraction based on the given operation.
  • Identify the variables in the problem.
  • Understand the operation (in this case, subtraction).
  • Combine the variables using the operation.

For the phrase 'the difference of \( m \) and \( n \)', we subtract \( n \) from \( m \), resulting in the algebraic expression \( m - n \). This is a basic yet essential part of mastering algebra, as identifying and manipulating variables forms the foundation for more complex topics.

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