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Chapter 2: Problem 23

For Exercises \(17-46,\) simplify \(-2-(-66)\)

Short Answer

Expert verified
64

Step by step solution

01

Understand the Problem

The given expression to simplify is -2-(-66). Notice that there is a double negative sign in the expression.
02

Apply the Double Negative Rule

A double negative (e.g., -(-a)) turns into a positive. Therefore, -2-(-66) can be rewritten as -2 + 66.
03

Perform the Addition

Now, add -2 and 66. This is straightforward: 66 - 2 = 64.
04

Write the Final Answer

The simplified form of the expression -2-(-66) is 64.

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Key Concepts

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

Double Negative Rule
A double negative in mathematics might be confusing at first, but it has a simple rule. When you come across two negative signs next to each other, they turn into a positive sign. For example, \[ -(-a) = +a.\]

This is because subtracting a negative number is the same as adding a positive number. Imagine you have an expression like \(-2-(-66)\).

Here, the double negative around 66 changes to a positive, turning the expression into \(-2 + 66\).

This rule is extremely helpful to simplify expressions and avoid mistakes.

Remember: Two negatives make a positive.
Integer Operations
Operations involving integers are basic but crucial in mathematics. Integers include all whole numbers, both positive and negative, including zero. When dealing with integer operations, you will come across addition, subtraction, multiplication, and division.

The key things to remember are:
  • Subtracting a positive is like adding a negative.
  • Subtracting a negative is like adding a positive.
  • Addition and multiplication of two integers with the same sign (either both positive or both negative) results in a positive integer.
  • Addition and multiplication of two integers with different signs (one positive and one negative) results in a negative integer.

Always keep these rules in mind, and integer operations will seem much easier!
Addition of Integers
Adding integers correctly is essential for solving many math problems. When adding integers:
  • If they have the same sign, add their absolute values and keep the sign.
  • If they have different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the larger absolute value.

In the given example, after applying the double negative rule, we had to add -2 and 66:
\(-2 + 66\).

Here, the integer 66 has a larger absolute value, so the sum is positive:
\(66 - 2 = 64\).

Thus, \(-2 - (-66) = 64\). Always double-check your signs and absolute values to ensure accurate results.

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Most popular questions from this chapter

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