Problem 70 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ -300-(-11) $$

Step-by-Step Solution

Answer

The result is -289.

Step 1: Identify the Operation

The problem given is \(-300 - (-11)\). This equation involves subtraction of a negative number.

Step 2: Rewrite Subtracting Negative as Addition

Subtraction of a negative number is equivalent to addition. Thus, rewrite the expression as:\[-300 - (-11) = -300 + 11\].

Step 3: Perform the Addition

To perform the addition, consider starting from \(-300\) and adding \(11\). Since \(11\) is positive, it can reduce the effect of the negative \(300\). Calculate:\[-300 + 11 = -289\].

Step 4: Confirm the Result

Check the work to ensure that adding \(11\) to \(-300\) indeed results in \(-289\). The calculation is correct since adding a smaller positive number to a larger negative number results in a less negative result.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are represented with a minus sign in front, like \(-1\), \(-15\), or \(-300\). Negative numbers are used to show values that are opposite to positive numbers or below a certain point. They often represent things like debts or temperatures below zero.

• They are placed to the left of zero on a number line.
• The further left they are, the smaller their value.
• Negative numbers decrease as you move to the left and increase as you move to the right towards zero.

Negative values are important in many math operations as they help in understanding directions and changes in amounts.

Subtraction of Negatives

Subtraction of negative numbers might seem tricky, but it actually turns into addition. When you see an equation like \(-300 - (-11)\), think of it as finding the difference between two numbers where one is negative. The important rule here is:

• Subtracting a negative is the same as adding a positive.

In our example, you take away negative \(-11\) from \(-300\). This can be confusing at first, but think about it this way:

• Subtracting a negative cancels out the negative sign, essentially flipping it into an addition.
• So, \(-300 - (-11)\) becomes \(-300 + 11\).

The new equation, \(-300 + 11\), simply reduces the amount of negative, making it less negative overall.

Addition of Integers

Adding integers can involve both positive and negative numbers. It requires understanding how each influences the other. When adding, pay attention to the signs:

• Adding a positive number to a negative number moves you closer to zero on the number line, potentially passing zero into positive territory.
• Adding two negative numbers makes the negative value larger, moving further from zero.

In the equation \(-300 + 11\), you begin with a negative number. Here's how it works:

• Start at \(-300\), which is the negative starting point.
• Then add \(+11\), which decreases the magnitude of negativity, bringing you closer to zero.

The final result, \(-289\), is closer to zero than the original \(-300\), because adding the positive integer \(+11\) has reduced the negative value slightly.