Problem 41 Explain how to evaluate an expre... [FREE SOLUTION]

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Chapter 3: Problem 41

Explain how to evaluate an expression. $$-2 m+n ; m=4, n=7$$

Short Answer

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Question: Evaluate the expression $$-2m + n$$ when m = 4 and n = 7. Answer: $$-1$$

Step by step solution

Write the expression

The expression to evaluate is: $$-2m + n$$

Substitute the given values for m and n

Now we will substitute the given values for m and n, which are m = 4 and n = 7: $$-2(4) + 7$$

Perform the multiplication

In this step, we'll multiply -2 and 4: $$-8 + 7$$

Perform the addition

Finally, we will add the remaining values: $$-1$$ So, after evaluating the expression $$-2m + n$$ with m = 4 and n = 7, we get the result: $$-1$$.

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Key Concepts

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

Substitution in Algebraic Expressions

Substitution is a fundamental concept in algebra that involves replacing variables in an expression with their respective values. This is often the first step in evaluating an expression. Let's consider the given expression $-2m + n$. Here, the variables 'm' and 'n' represent unknown quantities that were specified to be 4 and 7 respectively.
By substituting these known values into the algebraic expression, we create a numeric equation which can then be simplified further. In practice:

Identify the variables in the expression (in our example, 'm' and 'n').
Replace each variable with its assigned number. For this task, substitute 'm' with 4 and 'n' with 7, resulting in: $-2(4) + 7$.

This process transforms the original expression into a simpler form that can be easily calculated, making it a key step in simplifying and solving algebraic problems.

Order of Operations

The order of operations is a set of rules that determines the correct sequence to evaluate a mathematical expression. Without these rules, the same expression could yield different results depending on how it was calculated. The order can be remembered using the acronym PEMDAS:

Parentheses: Solve expressions inside brackets first.
Exponents: Evaluate powers and roots.
Multiplication and Division: Carry these operations out from left to right.
Addition and Subtraction: Also proceed from left to right.

In our expression $-2(4) + 7$, there are no parentheses that affect computation beyond the immediate step, so we skip to multiplication. According to the order of operations, multiply $-2$ by $4$ resulting in $-8$. Next, proceed to addition and calculate $-8 + 7$, which gives us $-1$. Adhering to the correct order prevents errors and ensures accuracy in the calculation.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of all mathematics, and mastering them is essential for evaluating any expression.In our problem, we utilize two of these operations:

Multiplication: The first operation applied is multiplying $-2$ by $4$ to get $-8$. Multiplication involves calculating the total of one number taken a specified number of times.
Addition: Next, we add $-8$ and $7$. Addition combines numbers into a sum. In this case, adding $-8$ to $7$ results in $-1$.

Each operation simplifies the expression step-by-step. Understanding how and when to perform these basic operations is crucial for solving more complex mathematical problems efficiently.

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91影视

Explain how to evaluate an expression. $$-2 m+n ; m=4, n=7$$

Short Answer

Step by step solution

Write the expression

Substitute the given values for m and n

Perform the multiplication

Perform the addition

Key Concepts

Substitution in Algebraic Expressions

Order of Operations

Basic Arithmetic Operations

One App. One Place for Learning.

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