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Chapter 1: Problem 39

\(-11-(-10)\)

Short Answer

Expert verified
The result is \(-1\).

Step by step solution

01

Recognize the Expression

The expression given is \(-11 - (-10)\). This is a subtraction problem involving negative numbers.
02

Apply the Rule for Subtracting Negatives

When you subtract a negative number, it is the same as adding its positive counterpart. Therefore, \(-11 - (-10)\) becomes \(-11 + 10\).
03

Perform the Addition

Now, perform the addition: \(-11 + 10\). This can be thought of as starting at \(-11\) on the number line and moving 10 units to the right, which brings us to \(-1\).

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers less than zero. They are often used to represent values below a certain reference point, like temperatures below freezing or a debt in a bank account. These numbers are indicated by a minus sign (-) before them. Negative numbers are located to the left of zero on the number line.
  • Example: -1, -2, -11
Visualizing negative numbers on a number line can help understand their behavior. When we move left from zero, the numbers decrease. Conversely, moving right brings us to larger numbers. Recognizing how negative numbers relate to positive ones is crucial in solving mathematical expressions.
Subtraction of Expressions
Subtraction in mathematics means finding the difference between two numbers or expressions. When dealing with negative numbers, subtraction can seem tricky, but there's a helpful rule: subtracting a negative number is equivalent to adding a positive number. This concept simplifies the solution process.
  • For instance:
    • The expression \(-11 - (-10)\) becomes \(-11 + 10\).
Remember this handy rule whenever dealing with negatives in subtraction. It allows one to convert the problem into an addition, which is often easier to solve.
Using the Number Line
A number line is a visual tool that helps us understand the order and distance of numbers. It's especially useful in operations involving negative and positive values. On a number line, we represent each number with a point.
  • Start at \(-11\).
    • From \(-11\), move 10 places to the right (since \-(-10)\ becomes \(+10)\).
    • You end up at \(-1\).
Using a number line to visualize expressions and movements between points can clarify the process and solution of problems involving mixed operations and negative numbers.

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Most popular questions from this chapter

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(-3 x+7 x+4 x-2 x-x\) for \(x=-13\)

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$17+(-18)-19-14+13-17$$

Simplify each algebraic expression by combining similar terms. $$3(a-1)-2(a-6)+4(a+5)$$

Explain the difference between a numerical expression and an algebraic expression.

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$-49(72)-49(28)$$
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