Problem 7 - Prealgebra

Question

Subtract. $$-4-1$$

Step-by-Step Solution

Answer

The result of -4 - 1 is -5.

Step 1: Identify the problem

The problem is to subtract 1 from -4, which can be represented as \(-4 - 1\).

Step 2: Rewrite the subtraction as adding a negative

In mathematics, subtracting a number is the same as adding its opposite. Therefore, it can be rewritten as \(-4 - 1 = -4 + (-1)\).

Step 3: Understand number line movement

When you add a negative number, it is like moving to the left on the number line. Start at -4 and move 1 unit to the left.

Step 4: Perform the calculation

Adding -1 to -4 (\(-4 + (-1)\)) results in -5. Therefore, \(-4 - 1 = -5\).

Step 5: Verify the result

To ensure the result is correct, re-evaluate by imagining starting at -4 and moving 1 step to the left (more negative). The position reached is indeed -5.

Key Concepts

Number Line Movement

When you work with integer subtraction, visualizing the process on a number line can be really helpful. Imagine a long line with zero in the middle. Positive numbers go to the right and negative numbers go to the left.

- Start at the number you are subtracting from, which in this case is -4.- If you subtract a positive number, you move to the left. Each step you take to the left represents subtracting 1.- For the exercise \(-4 - 1\), start at -4 on the number line and move 1 step to the left.

Picture yourself at -4. When you take that additional step to the left, you land at -5. This shows that \(-4 - 1 = -5\). Using the number line in this way makes it easier to see why subtracting moves you further into negative territory.

Adding Opposites

In math, subtraction of a number is like adding its opposite. This concept can simplify operations and help you understand calculations better.

- The opposite of a number is just the same number with a different sign.- Subtracting a positive number is the same as adding a negative number.

For instance, \(-4 - 1\) can be rewritten using this idea. You can change it into \(-4 + (-1)\), making it easier to deal with the operation. Why does this help?

• Addition is often simpler to manage mentally than subtraction.
• Visualizing often becomes easier, especially when using a number line.

Using the idea of adding opposites transforms a tricky subtraction problem into an addition problem, which many people find more straightforward.

Negative Numbers

Negative numbers are an essential part of math but can sometimes seem a bit tricky at first. Understanding how they interact with other numbers is key.

- Negative numbers are to the left of zero on a number line.- They are less than zero and represent values "less than nothing," such as debts or temperatures below freezing.- When you add a negative number, it moves you further left on the number line.

In the problem \(-4 - 1\), you begin with -4, a negative number. Subtracting another positive 1 effectively means you add -1 to it, moving you more into the negatives. Hence, you go left on the number line to -5.

Understanding negative numbers involves seeing how they behave both in isolation and in operations, especially as compared to positive numbers. Gaining this understanding helps to demystify integer subtraction.