Question

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 0-7 $$

Short answer

-7

Step-by-step solution

Rewrite subtraction as addition

The primary rule to convert a subtraction into an equivalent addition is the rule of 'adding a negative'. We can interpret the operation 0 - 7 as 0 + (-7).

Evaluate the addition expression

Next, we will proceed to evaluate the addition expression. When we add a negative number to 0, the result is just the negative number itself. Thus, 0 + (-7) equals to -7.

Key concepts

Rewriting Subtraction as Addition

Understanding the concept of rewriting subtraction as addition is fundamental in algebra. It simplifies calculations by converting a subtraction operation into an addition operation. The general rule is to take the number being subtracted, and instead add its opposite, which is also known as its additive inverse. For instance, the operation \( 0 - 7 \) can be viewed as \( 0 + (-7) \). This method is particularly useful as it allows us to handle the subtraction of negative numbers and variable expressions.

To ensure this concept is clearly understood, imagine you have a number line in front of you. Normally when you subtract, you move to the left on the number line. However, by rewriting subtraction as addition, you add a negative number, essentially moving to the left with the same effect. It comes down to this simple switch: whenever you see a subtraction sign, you interpret it as adding a negative instead.

Adding Negative Numbers

When it comes to adding negative numbers, the process is straightforward once grasped. Adding a negative number is essentially the same as subtraction. In practice, you're moving to the left on the number line. For example, if you're adding \( -7 \) to \( 0 \), you're starting at zero and moving seven places to the left, which leads you to \( -7 \). This principle applies universally, whether you're dealing with simple integers or complex algebraic expressions.

Here's another tip to remember: when adding two negative numbers together, like \( -3 + (-4) \), you add their absolute values (the positive versions) to get \(7\), but since both numbers were negative, the result is \( -7 \). The same concept also aids in visualizing the addition of positives and negatives, such as \( -3 + 4 \) where the higher absolute value dictates the sign of the answer.

Evaluating Expressions

Evaluating expressions is the final step where you apply arithmetic operations to simplify the expression to a single numerical value. After rewriting subtraction as addition and understanding how to add negative numbers, evaluating the sum becomes an application of basic arithmetic rules. In our example, evaluating \( 0 + (-7) \) results in \( -7 \).

It's good practice to work through expressions step by step. First, replace subtraction with addition of the negative equivalent, then combine like terms, and finally perform the arithmetic operations to obtain the result. Constant practice helps solidify the process of evaluating expressions until it becomes almost second nature, allowing you to tackle more complex algebraic problems with confidence.