Problem 64 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -7-(-5) $$

Step-by-Step Solution

Answer

-2

Step 1: Understand the Problem

We need to find the difference between -7 and -5.

Step 2: Rewrite the Subtraction

Rewrite the expression by changing the subtraction of a negative number into an addition: -7 - (-5) becomes -7 + 5.

Step 3: Perform the Addition

Now, perform the addition operation: -7 + 5 = -2.

Key Concepts

subtraction of negative numbers

When you encounter the subtraction of a negative number in algebra, it can be a bit tricky at first. But, it's actually quite straightforward once you understand the core idea.

Here’s a useful tip: subtracting a negative number is the same as adding its positive counterpart. In other words, to subtract a negative number, you can change the subtraction sign to an addition sign and make the negative number positive: \[ -7 - (-5) = -7 + 5 \]

It's like when two negative signs together in a mathematical operation 'neutralize' each other, resulting in a positive.

So whenever you face \[a - (-b)\] in algebra, simply turn it into \[a + b\] and the problem becomes much easier to handle!

addition in algebra

Addition in algebra involves combining numbers or variables in a simplified manner. Adding integers is a common task you will encounter. While performing addition, keep the following points in mind:

• Positive and positive = add the absolute values
• Negative and negative = add the absolute values and keep the negative sign
• Positive and negative = subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value

In the given exercise, when we rewrite \(-7 - (-5)\) as \(-7 + 5\), we follow the positive and negative rule stated above. \[ -7 + 5 = -2 \]
We subtract 5 from 7 and keep the sign of the number with the larger absolute value, which is -7. Hence, \(-2\) is our final answer.

integer operations

Integer operations form the backbone of algebraic calculations. Mastering how to add, subtract, multiply, and divide integers is essential for solving more complex algebra problems. Let’s focus on subtraction and addition here.

Key Points:

• Always pay attention to the signs of the integers.
• Use the rules of addition and subtraction to combine integers effectively.
• Remember that subtracting a negative number means you need to add its positive counterpart.

Here’s a quick review:

Subtraction: Change the subtraction of a negative to the addition of its positive.
Addition: Combine the integers by summing their absolute values if the signs are the same, or find the difference if the signs are different.

By practicing these integer operations, you’ll be more comfortable handling various algebraic problems.