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Chapter 2: Problem 25

For Exercises \(17-46,\) simplify $$-14-(-14)$$

Short Answer

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Step by step solution

01

Identify the arithmetic operation

Understand that the expression involves subtraction of a negative number: $$-14 - (-14)$$
02

Apply the rule for subtracting a negative number

When you subtract a negative number, it is the same as adding the positive of that number. Therefore, $$-14 - (-14) = -14 + 14$$
03

Simplify the expression

Perform the addition: $$-14 + 14 = 0$$

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Key Concepts

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

subtracting negative numbers
Subtracting negative numbers can be tricky, but it becomes simple once you understand the rule. When you subtract a negative number, you are essentially adding its positive counterpart. Think of it this way: the double negatives cancel out each other, resulting in a positive.

For example, consider the expression \[-14 - (-14)\]. The double negative turns into a plus: \[-14 + 14\]. This rule can be universally applied to any situation where you encounter the subtraction of a negative number. Remember:
  • Two negatives make a positive in subtraction
  • \(-a - (-b) = -a + b\)
By mastering this rule, you鈥檒l avoid common pitfalls and make your calculations much more straightforward.
integer operations
Integer operations are fundamental to arithmetic. Understanding how to work with integers, including positive, negative numbers, and zero, is crucial for simplifying expressions correctly.

Here are some key points:
  • Addition of two positive numbers yields a positive sum.
  • Addition of a positive and a negative number yields a sum that depends on their absolute values.
  • Subtraction can be converted into addition by adding the opposite (negative becomes positive).
  • Multiplication and division follow more straightforward rules: two same-signed numbers produce a positive result, while different signed numbers produce a negative result.
For instance, in the given exercise, converting \[-14 - (-14)\] into \[-14 + 14\] involves understanding integer operations and the conversion of subtraction into addition. Practice different integer operations to build a solid arithmetic foundation.
simplifying expressions
Simplifying expressions involves breaking down complex arithmetic sequences into more manageable steps.

Here鈥檚 how to approach it:
  • Identify the operations involved: prioritize parentheses and note any negative signs.
  • Apply rules for subtraction or addition of integers.
  • Perform arithmetic operations step-by-step and simplify the expression.
In the example \[-14 - (-14)\], breaking it down into \[-14 + 14\] and subsequently simplifying it to 0, we simplify the expression completely. Each step should reduce the complexity of the expression until you achieve the simplest form.

Remember: practice and repeated application of these rules will make simplification an intuitive process.

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Most popular questions from this chapter

Perform the indicated operation. $$24 \div(-2)$$

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Divide the real numbers, if possible. $$\frac{-56}{-8}$$
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