Problem 9 - Prealgebra

Question

Subtract. $$5-(-2)$$

Step-by-Step Solution

Answer

7

Step 1: Identify the Operation

The operation involves subtraction, specifically subtracting a negative number. The expression given is \(5 - (-2)\).

Step 2: Understand the Effect of Subtracting a Negative

Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, \(5 - (-2)\) is the same as \(5 + 2\).

Step 3: Perform the Addition

Now simply add the numbers: \(5 + 2\). This gives us \(7\).

Step 4: Write the Answer

Once you've completed the addition, you find that \(5 - (-2) = 7\).

Key Concepts

Understanding Negative Numbers

Negative numbers represent values that are less than zero. They are usually written with a minus sign (-) in front of them, like -1, -2, -3, etc. These numbers are essential in mathematics, especially when dealing with operations that involve values below zero or losses. Understanding negative numbers is crucial for solving problems in many areas including finance and science.
When we visualize negative numbers on a number line, they are to the left of zero. On this line, moving to the right means increasing in value, while moving to the left means decreasing. Thus, -3 is to the left of -1 and is smaller. This understanding helps when performing operations like subtraction and addition with negative numbers.

The Addition of Integers

Adding integers involves combining both positive and negative numbers. When you add a negative integer, it is like subtracting; while adding a positive integer means increasing the value. The rules are quite straightforward:

• If both integers are positive, you simply add them as usual.
• If both integers are negative, add their absolute values (ignore the minus sign) and then apply a negative sign to the result.
• If one positive and one negative, subtract the smaller absolute value from the larger absolute value, and keep the sign of the integer with the larger absolute value.

For example, to add -2 and 5, you compute 5 - 2 which equals 3. The number with the larger absolute value is positive, so the result stays positive. This understanding makes handling larger and more complex arithmetic operations involving integers much simpler.

Basic Algebraic Operations

Algebraic operations include addition, subtraction, multiplication, and division involving variables and numbers. These operations form the foundation of algebra, allowing us to solve equations and understand mathematical relationships. Subtracting numbers, as in this exercise, is one of these basic operations.
When subtracting numbers, especially negative ones, we use a helpful trick: subtracting a negative is equivalent to adding a positive. For instance, in the expression \(5 - (-2)\), we turn it into \(5 + 2\), resulting in 7. This simplification is crucial when dealing with algebraic expressions and equations. It helps maintain consistency when transitioning between different operations, ensuring clarity in more complex problems.
Understanding and applying these principles makes managing algebraic expressions much easier and equips students with the skills to tackle advanced mathematical challenges.