Problem 44 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 0-(-7) $$

Step-by-Step Solution

Answer

Answer: The result of 0 - (-7) is 7.

Step 1: Rewrite the subtraction expression as addition of the opposite number

To handle subtracting a negative number, we will rewrite the operation as adding the opposite of the number. In this case, the opposite of -7 is 7. So our expression becomes: $$ 0 + 7 $$

Step 2: Perform the addition

Now we simply add the two numbers (0 and 7) together: $$ 0 + 7 = 7 $$

Step 3: Write the final answer

The result of the operation 0 - (-7) is: $$ 7 $$

Key Concepts

Subtraction of Integers

Subtraction with integers can sometimes feel tricky, especially when negative numbers are involved. The key is understanding that subtracting an integer is the same as adding its opposite. For example, when you encounter expressions like \(0 - (-7)\), it might initially seem complex. However, by remembering the rule "subtracting a negative is like adding a positive," it becomes much more straightforward. So, in this case, \(0 - (-7)\) gets transformed into \(0 + 7\). This way of thinking helps simplify the calculation.

• Subtracting a positive number (e.g., 7) makes a number smaller.
• Subtracting a negative number (e.g., -7) makes a number larger because you add the absolute value.

Practice this approach with exercises to become more comfortable with integer operations.

Addition of Integers

Adding integers is usually more straightforward, but let's break it down so it's crystal clear. When dealing with integers, always remember these simple rules:

• Adding two positive integers gives a positive sum.
• Adding two negative integers gives a negative sum.
• Adding a positive integer and a negative integer involves taking their absolute values and subtracting the smaller from the larger, keeping the sign of the number with the larger absolute value.

For example, with the expression \(0 + 7\), it's straightforward: you simply add the numbers together to get 7. However, always be attentive to the signs of the numbers you're adding, as they dictate the final result.

Negative Numbers

Understanding negative numbers is essential in performing operations with integers. Negative numbers are integers less than zero, and they are typically marked with a minus sign (e.g., -1, -7). They may seem confusing at first because they represent values less than zero, often used to symbolize debts or losses.

• When you add a negative number to a positive number, you effectively subtract the absolute value of the negative number from the positive number.
• When you subtract a negative number, think of it as reversing a debt or loss, which results in a gain or increase in value.

For example, subtracting \(-7\) results in the equation \(0 - (-7)\), simplifying to \(0 + 7\) as subtracting a negative turns into a positive addition. Remember: negative numbers invert the typical meanings of addition and subtraction!