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Chapter 2: Problem 54

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$a+b+|c|$$

Short Answer

Expert verified
The value of the expression is 7.

Step by step solution

01

Substitute Given Values

Substitute the given values for each variable in the expression. Here, we replace \(a\) with \(0\), \(b\) with \(3\), and \(c\) with \(-4\). The expression becomes: \(0 + 3 + | -4 |\).
02

Evaluate Absolute Value

Calculate the absolute value of \(-4\). Absolute value is the distance from zero, so:\(|-4| = 4\).
03

Simplify the Expression

Now, with the absolute value calculated, substitute back into the expression:\(0 + 3 + 4\).
04

Perform the Addition

Finally, add the numbers together:\(0 + 3 + 4 = 7\).

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Key Concepts

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

Substitution in Expressions
Substitution in expressions is a fundamental concept in prealgebra that involves replacing variables with given values. This is like swapping placeholders for actual numbers. For example, in the expression \(a + b + |c|\), each letter represents a number. Here, \(a\) becomes \(0\), \(b\) becomes \(3\), and \(c\) becomes \(-4\).
This method allows you to transform abstract expressions into concrete numbers, making them easier to work with.
  • Identify the variables in the expression, such as \(a\), \(b\), and \(c\).
  • Find the given values for each variable.
  • Replace each variable in the expression with its corresponding value.
Once substituted, you replace the variable part of the math problem with known quantities, simplifying the problem-solving process.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of its direction. This means the absolute value always results in a non-negative number. In mathematical terms, the absolute value of a number \(x\) is denoted as \(|x|\). For example, \(|-4|\) is 4, because the distance from -4 to 0 is 4 units.
Understanding absolute value involves:
  • Recognizing that the absolute value discards any negative sign.
  • Rewriting negative numbers inside absolute value bars as positive.
  • Remembering that the absolute value of zero is zero, as it is at the origin of the number line.
Using absolute value can help simplify expressions and is crucial when dealing with both positive and negative numbers. It ensures values are treated as their "size" only, not their direction.
Arithmetic Operations
Arithmetic operations are the basic mathematical processes used to solve expressions. These include addition, subtraction, multiplication, and division. When you substitute values and simplify the expression, the next step is to perform arithmetic operations to find the final result.
For the expression \(0 + 3 + 4\):
  • First, add the first two numbers: \(0 + 3 = 3\).
  • Then, add the result to the next number: \(3 + 4 = 7\).
Using a structured approach by following the order of operations ensures that you evaluate the expression correctly. It's important to perform these operations carefully to arrive at the right answer. Arithmetic forms the foundation of all higher-level math, making it essential to master these operations early on.

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Most popular questions from this chapter

Translate each phrase into an algebraic expression. the sum of \(t\) and 9

Evaluate each expression. \(-16 c d,\) if \(c=4\) and \(d=-5\)

Evaluate each expression \(|7|\)

Simplify each expression. $$4(6 h)$$

Find each quotient. $$90 \div 15$$
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