Problem 19 - Algebra A Combined Function

Question

Subtract. \(-21-(-21)\)

Step-by-Step Solution

Answer

The result of \(-21 - (-21)\) is 0.

Step 1: Identify the Expression

The given expression is \(-21 - (-21)\). This means you are subtracting \(-21\) from \(-21\).

Step 2: Simplify the Double Negative

When you have a minus sign in front of a negative number, the two negatives make a positive. Therefore, \(-21 - (-21)\) simplifies to \(-21 + 21\).

Step 3: Perform the Addition

Now you have the expression \(-21 + 21\). Adding these two numbers means you start at \(-21\) on the number line and move 21 units to the right.

Step 4: Calculate the Result

After moving 21 units to the right from \(-21\), you'll end up at 0. Therefore, \(-21 + 21 = 0\).

Key Concepts

Double Negative

In mathematics, a double negative occurs when subtracting a negative number. This can seem a bit tricky at first, but it's actually very straightforward. When you have a situation like \(-a - (-b)\), you're really turning those two negative signs into a positive action.

Imagine you have something like \(-21 - (-21)\). The subtraction of a negative number \((-21)\) effectively becomes addition. This happens because the two negatives cancel each other out. Think of it like this: removing a negative is the same as adding a positive. So, \(-a - (-b)\) simplifies to \(-a + b\). You switch the subtraction of a negative into addition.

Understanding this concept of "double negative" not only simplifies expressions but also strengthens your algebraic skills. It's like flipping a light switch twice; it returns to its original state.

Simplifying Expressions

Simplifying expressions can make your calculations much easier. It's like clearing away the clutter to see the solution more clearly. In \(-21 - (-21)\), once you apply the double negative rule, the expression simplifies immediately.

After dealing with the double negatives, our expression \(-21 - (-21)\) changes to \(-21 + 21\). Recognizing and simplifying these expressions is crucial because it can often reduce more complex problems into more manageable steps.

It’s similar to untangling a mess of earbuds; once everything is straightened out, you can get right to listening. Don't rush this step; carefully simplify expressions to accurately solve the problem.

Number Line Addition

Number line addition is a visual way to understand integer addition and subtraction. It helps to see movements along a line rather than just dealing with abstract numbers.

Picture a number line with zero in the center, negative numbers to the left, and positive numbers to the right. When you add or subtract integers, you move along this line.

• Start at the first number: \(-21\) means you begin 21 units to the left of zero.
• Then, we add 21 by moving 21 units to the right.
• After moving, you land at 0.

This shows \(-21 + 21 = 0\).

Visualizing with a number line makes addition and subtraction more intuitive, especially when dealing with negative numbers like \(-21\) and \(+21\). It’s a tool that transforms abstract math into something we can "see," making it easier to understand.