Problem 16 - Algebra A Combined Function

Question

Subtract. \(-4-(-16)\)

Step-by-Step Solution

Answer

The result of \(-4 - (-16)\) is 12.

Step 1: Identify the Problem

We need to compute the result of subtracting \(-16\) from \(-4\). The expression given is \(-4 - (-16)\).

Step 2: Apply the Rule of Subtraction of Negative Numbers

When you subtract a negative number, it is the same as adding its positive counterpart. Therefore, \(-4 - (-16)\) becomes \(-4 + 16\).

Step 3: Simplify the Expression

Compute the result of \(-4 + 16\). When you add \(16\) to \(-4\), you are essentially moving \(16\) units to the right on the number line starting at \(-4\).

Step 4: Perform the Calculation

Starting at \(-4\), add \(16\): \(-4 + 16 = 12\).

Step 5: Interpret the Result

The final result of the subtraction \(-4 - (-16)\) is \(12\).

Key Concepts

Integer Operations

Integer operations involve basic arithmetic, such as addition, subtraction, multiplication, and division, with integers. Integers include all whole numbers and their negative equivalents, like -3, 0, and 4.

When dealing with subtraction of negative numbers, remember a key rule: subtracting a negative is the same as adding a positive. This often confuses learners until they practice and see it demonstrated.

• The expression a-b implies subtracting the integer b from a.
• If b is a negative number, a - (-b) turns into a + b.

Understanding this rule allows students to tackle complex problems involving integer operations. A simple example is the subtraction problem: a - (-b). This operation converts directly to addition: a + b.

Algebra Problem Solving

Algebra problem-solving often involves expressions with unknown values, numbers, and operations. To solve these, one needs to apply established rules and simplify the expression until it's easily calculable.

For example, with the algebraic expression \(-4 - (-16)\), we begin by identifying the need to subtract an integer. Subtraction of negative numbers follows a straightforward yet essential rule: transform the subtraction into an addition.

This rule relies on the property of opposites in algebra, essential for solving complex equations efficiently. In our specific problem,

• We rewrite \(-4 - (-16)\) as \(-4 + 16\).
• Next, we calculate the sum which resolves into an easy addition task after applying the negative subtraction rule.

Often, tackling algebra problems entails breaking the steps into manageable bits through simplification to enhance efficiency in calculations, similarly to the subtraction operation seen here.

Number Line Visualization

A number line is a great visual tool to understand integer operations, especially when dealing with negative numbers and subtraction. It provides a clear, visual means of understanding the position and movement of numbers.

Imagine you're positioned at \(-4\) on the number line. Subtracting a negative number, like \(-16\), shifts your position to the right, effectively adding positive direction to your movement.

• Begin at \(-4\),
• Move \(16\) places right,
• This results at positive \(12\).

Each movement along the number line corresponds to an operation on the integers. Viewing the subtraction of \(-16\) not as a literal subtraction but as a movement reinforces understanding that subtracting a negative adds to the original number.

Thus, a number line not only aids in visualizing operations but in solidifying the conceptual understanding of arithmetic computations among integers.