Problem 4 - Algebra 1

Question

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 4-5 $$

Step-by-Step Solution

Answer

The equivalent addition expression of \(4-5\) is \(4+(-5)\), and the result is -1

Step 1: Identify the subtraction expression

We have the expression \(4 - 5\)

Step 2: Use the subtraction rule to rewrite as an equivalent addition expression

The expression \(4 - 5\) can be rewritten using the subtraction rule. So, \(4 - 5\) becomes \(4 + (-5)\)

Step 3: Evaluate the addition expression

Adding 4 and -5 gives a result of -1

Key Concepts

Equivalent Addition Expression

When faced with subtraction involving positive and negative numbers, it can be helpful to consider equivalent addition expressions. The subtraction rule functions as a bridge between subtraction and addition, making some calculations easier to manage, especially when dealing with negative numbers.

For instance, the subtraction expression \(4 - 5\) may not be as straightforward for some students, but by applying the subtraction rule, we can transform it into the equivalent addition expression \(4 + (-5)\). This approach is very effective because it simplifies the process of combining numbers with different signs. It effectively means that we're adding a negative quantity—that is, moving to the left on the number line from our starting point—which we can think of as subtracting a positive quantity.

Evaluating Expressions

Evaluating expressions is a foundational skill in algebra, which includes performing operations according to established mathematical rules. When we evaluate expressions that have been converted to equivalent addition expressions, we simply add the numbers together while keeping in mind the rules for adding positive and negative numbers.

Following the equivalent expression \(4 + (-5)\), as students, we perform the addition by combining the 4 and the -5. Since one is positive and the other is negative and they have different absolute values, we subtract the smaller absolute value from the larger one, keeping the sign of the number with the larger absolute value. The final value of the expression \(4 + (-5)\) is thus \-1\. This kind of evaluation helps students develop a more tangible and practical understanding of working with negative numbers in different contexts.

Negative Numbers

Negative numbers are an integral part of the number system and represent quantities less than zero. They appear often in algebra, especially in operations involving subtraction and addition across zero. Recognizing the implications of negative numbers is essential for accurately evaluating expressions.

In our example expression \(4 - 5\), the -5 is a negative number which represents a value of 5 units below zero. When these numbers are visualized on a number line, it can help students grasp that adding a negative number is akin to subtraction. That's why when we calculate \(4 + (-5)\), we're essentially moving from the position of 4 on the number line five units to the left, resulting in \-1\. This practical understanding of negative numbers not only simplifies the computational aspect but also deepens comprehension of the underlying concepts.