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Chapter 2: Problem 74

Write each phrase as an algebraic expression. The difference of \(m\) and \(-5\)

Short Answer

Expert verified
\( m + 5 \)

Step by step solution

01

Understand Key Terms

Identify the key mathematical terms in the phrase 'The difference of m and -5'. The term 'difference' means subtraction.
02

Identify the Variables and Constants

Determine the variables and constants. Here, the variable is 'm' and the constant is '-5'.
03

Formulate the Expression

Since 'difference' indicates subtraction, write the expression as \( m - (-5) \).
04

Simplify the Expression

Subtracting a negative number is the same as adding its positive counterpart: \( m - (-5) = m + 5 \).

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Key Concepts

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

subtraction in algebra
In algebra, subtraction is often represented by the term 'difference'.
When you see the word 'difference', it tells you to subtract one value from another.
For example, in the phrase 'The difference of m and -5', you're being asked to subtract -5 from m.
This can sometimes be tricky because subtracting a negative number is a bit different from regular subtraction.
When you subtract a negative number, you actually add the positive version of that number.
So, in our example, instead of subtracting -5, you add 5.
That's why the expression changes from m - (-5) to m + 5.
Understanding this concept is crucial as it's a common operation in algebra.
variables and constants
In algebra, we often work with variables and constants.
A variable is a symbol, like 'm', that represents an unknown value.
Variables can change depending on the problem.
On the other hand, a constant is a fixed value that doesn't change.
In our example, -5 is a constant because its value remains the same.
Recognizing the difference between these two is important when forming algebraic expressions.
It helps you know what you're working with and how to manipulate them.
Always remember, variables can change, but constants stay the same.
simplifying expressions
Simplifying expressions makes them easier to work with.
It involves combining like terms and performing basic arithmetic operations.
In our example, we started with the expression m - (-5).
By recognizing that subtracting a negative is the same as adding, we simplify it to m + 5.
Simplification is about making an expression more straightforward while keeping its value the same.
This process is essential for solving equations and understanding more complex algebraic concepts.
By practicing simplification, you'll become more comfortable and efficient in solving algebra problems.

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Most popular questions from this chapter

Find the range. The range of a set of numbers is the difference between the highest value and the lowest value. That is, range = highest - lowest. Find two integers whose difference is \(-6 .\) Answers may vary.

When a severe winter storm moved through Albany, New York, the change in temperature between 4: 00 P.M. and 7: 00 P.M. was \(-27^{\circ} \mathrm{F}\). What was the average hourly change in temperature?

Divide the real numbers, if possible. $$60 \div(-3)$$

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