Problem 112 - Algebra 1

Question

EVALUATING EXPRESSIONS Evaluate the expression. $$ 20+(-16)+(-3) $$

Step-by-Step Solution

Answer

The evaluated value of the expression \(20+(-16)+(-3)\) is \(1\).

Step 1: Simplify the expression

As the negative sign is indicative of subtracting that number from the given total. Therefore, the expression can literally read as 20 minus 16 and then subtract 3. That means we can re-write the expression as \(20 - 16 - 3\).

Step 2: Perform Subtraction

We start by subtracting 16 from 20 which give us 4 and then further subtract 3 from the result. That means, \(20 - 16 = 4\) and then \(4 - 3 = 1.\)

Step 3: Write out the solution

The result of the above calculations indicate that the value of the given expression \(20+(-16)+(-3)\) is \(1\)

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-) in front of them. Negative numbers are important in various mathematical operations, especially in subtraction and other calculations.
For example, when we have an expression like "+(-16)", it means we are adding a negative number, which is the same as subtracting that number from the original total.
Here are some key points about negative numbers:

• They appear on the left side of zero on a number line.
• Adding a negative number is the same as subtracting its positive counterpart.
• When you subtract a negative number, it is equivalent to adding that positive number.

In the exercise, "20 + (-16)" is interpreted as subtracting 16 from 20, leading us into understanding subtraction with negative numbers.

The Process of Subtraction in Arithmetic

Subtraction is one of the four basic arithmetic operations, and it's the process of taking one number away from another. In the context of evaluating expressions like the one given, subtraction is performed step by step to simplify calculations.
Here's what happens when you subtract:

• Identify the two numbers: the minuend (the number from which another number is subtracted) and the subtrahend (the number that is to be subtracted).
• Subtract the subtrahend from the minuend.
• Solve step by step, especially when working with multiple subtractions.

In our expression, we first perform the subtraction "20 - 16", which results in 4. Then subtract 3 from 4 resulting in the final answer, 1. This step-by-step approach ensures each operation is easily manageable.

Combining Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. In many expressions, you work with more than one operation at a time, and understanding these combined processes is essential to correctly evaluating such expressions.
When dealing with expressions involving both addition and subtraction, remember the following:

• Order of operations, sometimes remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• In our example, addition and subtraction are performed from left to right.
• Always simplify negative numbers appropriately by interpreting "+ (-)" as a subtraction operation.

In the given task, we dealt with adding negative numbers as a form of subtraction, thus simplifying it step-by-step. Recognizing patterns and rewriting expressions can help streamline these arithmetic evaluations.