Problem 3 - Algebra 1

Question

Explain the steps you would take to evaluate the expression \(5-7-(-4)\)

Step-by-Step Solution

Answer

The final answer after evaluating the expression \(5-7-(-4)\) is 2

Step 1: Understanding the Problem

The expression given is \(5 - 7 - (-4)\). The numbers are being subtracted. The special scenario here is the last part, where 4 is being subtracted, and it has a negative sign. The minus sign before the parentheses multiplies with the negative number inside, which results in a positive number.

Step 2: Apply Subtraction of First Two Numbers

Now subtract the first two numbers, which gives \(5 - 7 = -2\).

Step 3: Handle Negative of Negative Four

-(-4) is equal to +4. When a negative sign is placed before a negative number, it results in a positive number.

Step 4: Subtraction

Now, we can subtract -2 (from step 2) and 4 (from step 3) which results in \(-2 + 4 = 2\)

Key Concepts

Subtraction

Subtraction is one of the basic operations in mathematics that involves taking away a quantity from another.
Subtraction is represented by the minus sign "−" and can be applied to both positive and negative numbers.
In any subtraction problem, it is crucial to align numbers correctly and manage the signs appropriately.
To subtract two numbers, follow these steps:

• Identify the minuend (the first number from which you subtract).
• Identify the subtrahend (the number you are subtracting).
• Apply the minus sign to the subtrahend with caution, especially when negative numbers are involved.

The biggest challenge in a subtraction problem like \(5 - 7 - (-4)\) is managing how negative signs impact the calculation.
Understanding this is the key to correctly evaluating expressions involving subtraction and negative numbers.

Negative Numbers

Negative numbers are values less than zero and are denoted by a minus sign "-" before the number itself.
They play a critical role in various calculations, especially in subtraction and other operations involving integers.
When dealing with negative numbers, remember:

• Negative numbers are essentially the opposite of their positive counterparts.
• Subtracting a negative number is equivalent to adding a positive number.
• Two negative signs next to each other result in a positive when simplifying.

For example, in the expression \(5 - 7 - (-4)\), the subtraction of \(-4\) turns into addition because of the double negative, leading to \(+4\).
This concept is foundational when manipulating algebraic expressions or performing operations with integers.

Integer Operations

Integer operations encompass addition, subtraction, multiplication, and division involving whole numbers, both positive and negative.
When performing integer operations, the rule of signs is essential to follow:

• Addition: Adding integers follows rules similar to whole numbers, where you combine values, considering their signs.
• Subtraction: Convert the subtraction of a negative number to addition.
• Multiplication/Division: Same sign gets a positive result; different signs yield a negative result.

Understanding these operations is crucial for simplifying expressions like \(5 - 7 - (-4)\).
The expression initially seems complex due to the mix of positive and negative numbers but simplifies to\(5 - 7 + 4\) by correctly applying integer rules.
A solid grasp of integer operations ensures accurate and efficient problem-solving in algebra.