Problem 65 - Beginning and Intermediate Algebra

Question

Find each difference. $$ 2-(3-5) $$

Step-by-Step Solution

Answer

4

Step 1: Understand the expression

The expression to solve is 2 - (3 - 5). Notice it includes both subtraction and parentheses.

Step 2: Simplify inside the parentheses

First, solve the operation inside the parentheses: 3 - 5. Subtract 5 from 3 to get -2.

Step 3: Rewrite the expression

After simplifying inside the parentheses, replace the original expression with the result: 2 - (-2).

Step 4: Subtract the numbers

Subtracting a negative number is the same as adding its positive counterpart. Therefore, 2 - (-2) simplifies to 2 + 2.

Step 5: Final calculation

Add the numbers to get the final answer: 2 + 2 = 4.

Key Concepts

Basic Algebra

In algebra, we use symbols and letters to represent numbers in equations and expressions. It's important to understand these representations to solve algebraic problems. Basic algebra involves a few key operations:

• Addition
• Subtraction
• Multiplication
• Division

In our exercise, we're dealing with subtraction. Learning how to work with these basic operations forms the foundation for more complex algebraic concepts.

For example, let's look at the expression:
\text{\( 2 - (3 - 5) \)}
This shows how numbers and operators can be combined in a meaningful way to find a difference. Notice the use of subtraction and parentheses. Simplifying the expression step-by-step is crucial in solving the problem correctly.

Subtraction

Subtraction is one of the fundamental operations in math. When you subtract, you're finding the difference between two numbers. Here are some important things to keep in mind:

• Subtracting a larger number from a smaller one results in a negative number. Example: \text{\( 3 - 5 = -2 \)}.
• Subtracting a negative number is the same as adding its positive counterpart. Example: \text{\( 2 - (-2) = 2 + 2 \)}.
• Always perform subtraction from left to right in an expression unless parentheses dictate otherwise.

In our exercise, the expression inside the parentheses is simplified first:
\text{\( 3 - 5 = -2 \)}
This gives us:
\text{\( 2 - (-2) \)}

Which simplifies to \text{\( 2 + 2 \)}. Subtraction might seem simple on the surface, but it requires careful attention, especially when dealing with negative numbers and parentheses.

Parentheses in Math

Parentheses play a crucial role in mathematics by dictating the order of operations. They ensure that parts of an expression are evaluated first, which can change the outcome of the calculation. Here are some rules for using parentheses effectively:

• Always perform operations inside parentheses first.
• If multiple sets of parentheses are nested, start with the innermost set.
• Parentheses can clarify how complex expressions should be interpreted.

Applying these rules to our exercise:
\text{\( 2 - (3 - 5) \)}
means we first tackle the expression inside the parentheses:
\text{\( 3 - 5 \)}
Then, simplify the entire expression:
\text{\( 2 - (-2) \)}
which further simplifies to:
\text{\( 2 + 2 \)}.
Parentheses help avoid ambiguity and errors in mathematical calculations by ensuring we follow the correct order of operations.