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Chapter 13: Problem 45

Evaluate each expression if \(a=-2, b=-6,\) and \(c=14\) $$a-c$$

Short Answer

Expert verified
The value of the expression \(a - c\) is \(-16\).

Step by step solution

01

Substitute the Given Values

Start by replacing the variables in the expression with their given values. The expression is \(a - c\), and we know that \(a = -2\) and \(c = 14\). So, substitute these values in: \((-2) - (14)\).
02

Simplify the Expression

Simplify the expression by subtracting \(14\) from \(-2\). Think of this as moving 14 steps to the left on the number line from -2: \(-2 - 14 = -16\).

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Key Concepts

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

Subtraction
Subtraction is one of the fundamental arithmetic operations that involves taking away a quantity from another. When you perform subtraction, you're essentially finding the difference between two numbers. In our exercise, we explored subtracting 14 from -2 written as \(-2 - 14\). This gives us -16 as \(-2 - 14 = -16\).
  • Identify the numbers involved. We subtract the second number from the first.
  • For negative and positive numbers, subtraction can indicate movement towards more negative values on the number line.
For example, subtracting 14 from -2 decreases the value, moving further down the negative scale. It's crucial to treat subtraction as moving leftward or into larger negative values, especially when the numbers involved are negative or vary in sign.
Evaluating Expressions
Evaluating expressions means calculating the numerical value of a mathematical phrase. This usually involves replacing variables with their given values and performing arithmetic operations like addition, subtraction, multiplication, and division in the correct order.To evaluate the expression \(a - c\) when given \(a = -2\) and \(c = 14\):
  • First, substitute the values: replace \(a\) with \(-2\) and \(c\) with \(14\).
  • The expression becomes \((-2) - (14)\).
  • Finally, perform the arithmetic operation to get the result: \(-16\).
Substitution is a key part of evaluating expressions. Ensure each variable is correctly replaced, as mistakes here can lead to incorrect results.
Number Line
A number line is a visual representation of numbers on a straight line, where each point corresponds to a number. It helps to illustrate calculations such as addition and subtraction by showing movements along the line.In the context of our exercise, to solve \(-2 - 14\), imagine starting at \(-2\) on the number line:
  • Move 14 steps to the left (since we're subtracting 14), ending up at \(-16\).
Using a number line for subtraction shows how the numbers shift lower or higher, aiding comprehension. It's particularly helpful in grasping negative number concepts, as moving left deepens negativity and moving right decreases it.

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