Problem 28 - Prealgebra

Question

Subtract. $$-29-(-4)$$

Step-by-Step Solution

Answer

The result of \(-29 - (-4)\) is \(-25\).

Step 1: Understand the Expression

The expression given is the subtraction of two integers: \(-29 - (-4)\).Here, we are subtracting \(-4\) from \(-29\).

Step 2: Apply the Rule of Subtracting Negative Numbers

When subtracting a negative number, we turn the subtraction operation into an addition operation. Therefore, \(-29 - (-4)\) becomes \(-29 + 4\).

Step 3: Perform the Addition

Now that our problem is simplified to an addition, we calculate: \(-29 + 4 = ?\). Start from \(-29\) and count up 4 units: \(-28, -27, -26, -25\). Thus, \(-29 + 4 = -25\).

Key Concepts

Subtracting Negative Numbers

When we talk about subtracting negative numbers, it means we are dealing with two negatives inside a subtraction problem. Consider the original expression:

• \(-29 - (-4)\)

Here's a handy rule to remember: when you subtract a negative number, it is the same as adding a positive number. This is because a double negative (two negatives) turns into a positive.
For instance, the negative sign before \(-4\) turns the operation into addition, changing the expression to:

• \(-29 + 4\)

This simplification can help make the calculation much easier.
Understanding this rule will make dealing with negative numbers much less confusing.

Integer Addition

Integer addition includes combining both positive and negative numbers. With the expression now as

• \(-29 + 4\)

we focus on how to calculate using the integer addition rule.
When you have a negative integer and add a positive integer, it's like moving along a number line:

• Start at \(-29\)
• Move to the right by 4 steps to account for adding 4

This movement gives us:

• \(-28, -27, -26, -25\)

And so, the sum of \(-29\) and \(4\) is \(-25\). Understanding how to add integers whether they are negative or positive is key to solving many math problems correctly.

Negative Number Operations

Negative number operations involve adding, subtracting, multiplying, or dividing numbers with negative signs. A key point is noting how the signs interact with each other:

• Two negatives make a positive when subtracting: \(a - (-b) = a + b\).
• If both numbers have the same sign while adding or subtracting, you only focus on the difference in their values.

For instance, in the original problem, facing

• \(-29 - (-4)\)

is really a case of two negatives making a positive.
By converting the problem into an addition,

• \(-29 + 4\),

negative number operations become easier to handle, and the process simplifies to basic addition or subtraction of positive numbers. Mastery of these operations forms the foundation for more advanced mathematical concepts.