Problem 5 - Algebra 1

Question

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ 3-(-8) $$

Step-by-Step Solution

Answer

The equivalent addition expression to \(3-(-8)\) is \(3+8\) and the evaluated result of the expression is \(11\)

Step 1: Rewrite the Subtraction as Addition

Apply the subtraction rule, which states that subtracting a number is the same as adding its opposite. The expression becomes \(3 + 8\)

Step 2: Evaluation

Now, simply perform the addition: \(3 + 8 = 11\)

Key Concepts

Equivalent Expressions

When tackling math problems, you often encounter the term "equivalent expressions." Understanding this concept is fundamental. Equivalent expressions are different expressions that denote the same number or value. In simpler terms, they look different but have the same outcome.

In the context of subtraction, we can transform a subtraction expression into an equivalent addition expression by using the subtraction rule. The key is to remember that subtracting a negative is the same as adding a positive.

Consider the example \(3 - (-8)\):

• By the subtraction rule, this can be rewritten as \(3 + 8\).
• These two expressions - \(3 - (-8)\) and \(3 + 8\) - are equivalent because they represent the same value.

Recognizing and creating these equivalent expressions can simplify complicated problems, making it easier to find a solution.

Integer Addition

Adding integers is one of the fundamental operations in mathematics, and it's surprisingly straightforward. When working with integers, there are several simple rules to keep in mind:

• Adding two positive integers results in a positive sum.
• Adding two negative integers gives a negative sum.
• When you add a positive integer to a negative integer, you subtract their absolute values, and the sign of the result will depend on which number had a larger absolute value.

In the example \(3 + 8\), both numbers are positive integers. Hence, you simply add them:

• The sum of \(3\) and \(8\) is \(11\).

This shows how using integer addition can simplify evaluating expressions once you understand and convert them into equivalent expressions using the subtraction rule.

Evaluating Expressions

Evaluating expressions involves calculating the value of the expression using the rules of arithmetic. It sounds complex, but it becomes easy with a step-by-step approach.

For our example, once we rewrote \(3 - (-8)\) using the subtraction rule, the expression became \(3 + 8\). Now, evaluating this addition expression is straightforward:

• Add \(3\) and \(8\) to get the result \(11\).
• This final number, \(11\), is the evaluation of the expression \(3 - (-8)\).

To evaluate expressions effectively:

• Follow the order of operations, although for simple expressions like this one, understanding basic integer addition suffices.
• Practice transforming expressions where needed, noticing patterns like converting subtraction into addition.

By taking each step methodically, evaluating expressions becomes a much more manageable task.