Problem 29 - Algebra A Combined Function

Question

Add. See Examples 1 through 12,18, and 19. $$ 117+(-79) $$

Step-by-Step Solution

Answer

117 + (-79) = 38.

Step 1: Identify the Operation

In the given problem, we are asked to add two numbers: 117 and -79.

Step 2: Understand Adding a Negative Number

When adding a negative number, it's equivalent to subtracting the absolute value of that number. Thus, adding -79 is the same as subtracting 79.

Step 3: Perform the Subtraction

Subtract the absolute value of -79, which is 79, from 117. Calculate: 117 - 79.

Step 4: Calculate the Result

Perform the calculation: \[ 117 - 79 = 38 \]So, the result of adding 117 and -79 is 38.

Key Concepts

Addition Operation

When we talk about the addition operation, we're referring to the process of combining two or more quantities. It’s one of the four fundamental arithmetic operations. The result of addition is known as the sum. In the exercise provided, the operation is adding: 117 and -79. Addition can involve both positive and negative numbers, and it’s essential to understand how they interact.

• When both numbers are positive, the sum is straightforwardly obtained by adding them together.
• If both numbers are negative, the sum will also be negative, and it's found by adding their absolute values.

Understanding these basics of addition lays the groundwork for solving equations involving all kinds of numbers.

Negative Numbers

Negative numbers are numbers with a value less than zero, often used to represent loss, debt, or decrease. In the context of addition, negative numbers can change the direction of the operation. For instance, when you see an expression like 117 + (-79), the negative number is signaling a decrease or a subtraction from the positive number.

• Negative numbers are denoted with a minus sign (-) in front of them.
• They follow the same arithmetic rules as positive numbers, though their placement in equations alters the outcome slightly.

Knowing how to work with negative numbers is crucial as it forms the basis for understanding many algebraic concepts.

Absolute Value

The absolute value of a number refers to its distance from zero on the number line, regardless of direction. It turns a negative number into a positive number, which is useful in operations like addition and subtraction. For example, the absolute value of -79 is 79.

• Absolute values are always non-negative.
• They help simplify expressions by removing the effects of negative signs temporarily.

Using absolute values allows for straightforward comparison and calculation, particularly when dealing with complex expressions.

Subtraction

Subtraction is the process of removing a quantity from another. When adding a negative number, as in the problem of 117 + (-79), you effectively perform subtraction. This means subtracting 79 from 117 instead of adding. Understanding this concept can be very helpful.

• Subtraction can be thought of as the opposite of addition.
• It is crucial when transitioning from abstract mathematical concepts to real-world situations, like balancing budgets or inventories.

By mastering subtraction in the context of adding negative numbers, you can handle a wider variety of arithmetic problems with ease.