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Chapter 1: Problem 1

In Exercises \(1-72\), compute the value of each expression. $$6-(+10)$$

Short Answer

Expert verified
The value is \(-4\).

Step by step solution

01

Identify the Expression

The given expression is \(6-(+10)\).
02

Simplify the Expression

Rewrite the expression to make it simpler to solve. Remember that subtraction can be thought of as adding a negative number. So, the expression \(6-(+10)\) can be rewritten as \(6+(-10)\).
03

Perform the Addition

Now, add the two numbers: \(6 + (-10)\). When you add a negative number, it's the same as subtracting that number from the first number. Therefore, \(6 + (-10) = 6 - 10\).
04

Calculate the Result

Subtract 10 from 6: \(6 - 10 = -4\).

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Key Concepts

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

Addition of Negative Numbers
When you see a problem involving the addition of negative numbers, it can seem confusing at first. But it's actually quite simple once you understand the rules.
Let's look at the expression from our example: 6 - (+10).
First, note that subtracting a positive number is the same as adding its negative counterpart.
So, 6 - (+10) can be rewritten as 6 + (-10).
This may look unusual if you're not used to negative numbers, but it becomes easier with practice.
When you add a negative number, think of it as moving to the left on the number line.
  • If you start at 6 and move 10 steps to the left, you land at -4.
Therefore, 6 + (-10) equals -4. Remember: adding a negative number results in a smaller number than you started with.
Subtraction
Subtraction is one of the basic arithmetic operations. It often confuses students because it's closely related to addition.
In the expression 6 - 10, we simply start at 6 and move 10 units to the left on the number line.
Let's break down the subtraction steps with a practical approach:
  • Start with the number 6
      If we count backwards by 10 steps (subtracting 10),
        we pass 0 and reach -4.
This is how the subtraction of 10 from 6 results in -4.
Subtraction essentially measures the difference between two numbers where you take away the value of the second number from the first.
Simplification of Expressions
Simplification of expressions uses arithmetic rules to make calculations easier.
In the example we have, 6 - (+10), simplifying helps us understand the problem better.
Start by rewriting the expression. The crucial part in simplification here is:
  • Subtraction can be translated to addition of a negative number:
      6 - (+10) becomes 6 + (-10)
This step converts what might look complex or confusing into a familiar addition problem.
Once simplified, steps become clear and manageable:
  • Identify the starting number
    • (in this case, 6)
  • Add the negative number
    • (10 units to the left)

    The result is easier to compute and understand once the expression is simplified.
    This helps prevent mistakes and makes it easier to follow through to the correct answer. Simplifying expressions forms the foundation for solving more complex problems with confidence.

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Most popular questions from this chapter

In Exercises \(1-66,\) compute the value of each expression. $$-29+(-31)+51$$

In Exercises \(1-72\), compute the value of each expression. $$52-(-38)-67$$

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On a certain day the maximum temperature was \(12^{\circ} \mathrm{C},\) and the minimum temperature was \(-5^{\circ} \mathrm{C} .\) By how many degrees did the temperature vary on this day?

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