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Chapter 5: Problem 40

Perform the indicated subtraction. \(-19-(-2)\)

Short Answer

Expert verified
The result of the operation \(-19 - (-2)\) is \(-17\).

Step by step solution

01

Convert the Operation

The expression given is \(-19 - (-2)\). To simplify this, remember the rule of signs that says minus a negative becomes a positive. The equation therefore changes to \(-19 + 2\).
02

Perform the Addition

Now, proceed with addition to obtain the result. The operation becomes: \(-19 + 2 = -17\).

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Key Concepts

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

Subtraction
In mathematics, subtraction is one of the fundamental operations. When you subtract one number from another, it means you are finding the difference between the two. In simple terms, subtraction is taking away a number, known as the subtrahend, from another number, known as the minuend.
  • The result of subtraction is called the difference.
  • Subtracting a larger number from a smaller one will yield a negative result.
  • Subtraction is the opposite of addition.
When performing subtraction, it鈥檚 crucial to understand how the operation changes when negative numbers are involved. For instance, subtracting a negative is equivalent to adding a positive, which leads us to the next concept.
Negative Numbers
Negative numbers are integers that represent values less than zero. Depicted with a minus ( (-) ) sign, they are essential in various math operations. Understanding how negative numbers interact in arithmetic operations, like subtraction and addition, simplifies solving complex problems.
  • A negative number represents a deficiency or a reduction.
  • In a number line, negative numbers appear to the left of zero.
  • Subtracting a negative number is effectively adding the positive equivalent of that number.
Applying these principles helps interpret expressions like (-19 - (-2)) correctly. Here, since minus a negative is a positive, the equation transforms into a simple addition problem.
Addition
Addition is a basic arithmetic operation that involves calculating the total of two or more numbers. When you perform addition, you are essentially combining numbers to make a larger number.
  • Addition is commutative: changing the order does not change the sum. For instance, (a + b = b + a) .
  • The additive identity is zero, where adding zero to any number leaves it unchanged.
  • To add two integers, you align them according to their signs.
In the problem (-19 + 2) , addition comes after transforming (-19 - (-2)) , as subtracting a negative is equivalent to adding. The result, (-17) , showcases how addition helps simplify operations involving negative numbers.

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3, r=-2\)

What is an arithmetic sequence? Give an example with your description.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{5}, r=\frac{1}{2}\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{7}\), when \(a_{1}=5, r=-2\).
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