Problem 13 - Prealgebra

Question

Subtract. $$-4-(-7)$$

Step-by-Step Solution

Answer

The result of \(-4 - (-7)\) is 3.

Step 1: Identify the Terms

The expression given is \(-4 - (-7)\). In this expression, you need to subtract the second term \( -7 \) from the first term \( -4 \).

Step 2: Change the Double Negative

When you have a double negative, like \(-(-7)\), this becomes a positive. So the expression \(-4 - (-7)\) simplifies to \(-4 + 7\).

Step 3: Perform the Addition

Now calculate the result of \(-4 + 7\). When you add 7 to -4, you start at -4 on the number line and move 7 units to the right, which results in 3.

Key Concepts

Double Negative Simplification

A fundamental rule in mathematics is that two negative signs turn into a positive sign. This concept, known as double negative simplification, can sometimes confuse students, but it is straightforward once you get the hang of it.
Imagine you have - - ("- -") together. In the given expression -4 - (-7), notice the double negative in the parentheses. This can be simplified:

• -(-7) becomes +7.

This transformation changes the entire expression from -4 - (-7) to -4 + 7.
The rule can be remembered as: minus a negative is the same as adding. Think of it as taking away an obligation to subtract—a negative of a negative becomes a positive.

Number Line Addition

Number lines are a handy visual tool when learning addition and subtraction, particularly with integers. They help in visualizing the position of numbers and the distance between them, which is invaluable for number line addition.
In the expression -4 + 7:

• We start from -4 on the number line.
• Since we're adding 7, we move 7 spaces to the right.

Picture each step as moving one unit to the right. After moving 7 units right of -4, we land at +3.
This visual aid simplifies understanding how negative and positive numbers interact on the number line. It can be practiced with other similar problems to reinforce this skill further.

Integer Operations

Working with integers can seem a bit tricky at first, especially when dealing with negative numbers. However, understanding integer operations is crucial for mastering arithmetic.
When subtracting integers, remember:

• "Subtracting a negative" is the same as adding a positive.
• Positive + Positive = More Positive.
• Negative + Positive: start with the larger number's sign and subtract the smaller from the larger.

Subtraction and addition of integers rely on these principles. Let's apply it to our expression: -4 + 7.

• Think of it as noticing who "wins" in terms of size.
• 7 is larger than 4, so the result will take the sign of the larger number.
• Thus, -4 + 7 = 3.

The takeaway? Always adjust the operation under basic rules and use the number line to verify your work.