Problem 51 - Algebra 1

Question

Evaluate the expression. \(20+(-17)-8\)

Step-by-Step Solution

Answer

The expression \(20+(-17)-8\) equals -5.

Step 1: Identify the operations

The expression given is \(20+(-17)-8\). This involves one addition operation and one subtraction operation. The numbers involved are 20, -17 and 8.

Step 2: Perform the addition

Start by adding 20 and -17. When you add a negative number, it's like subtracting that number. So, \(20+(-17)\) is the same as \(20-17\), which equals 3.

Step 3: Perform the subtraction

Now, subtract 8 from the result of our previous step. So the expression becomes \(3-8\). When you subtract a larger number from a smaller number, the result is a negative number. So, \(3-8\) equals -5.

Key Concepts

Addition and Subtraction

When we work with arithmetic expressions, understanding how to perform addition and subtraction is crucial. These two operations are among the most fundamental of all mathematical tasks. Here's a simple breakdown:

• **Addition** is about combining numbers to get a total sum. It's the process of increasing a number. For example, adding 5 and 3 gives us 8.
• **Subtraction** is the process of taking one number away from another. It's about finding the difference between numbers. For instance, 8 minus 3 equals 5.

In the expression provided, 20, -17, and 8 are connected through addition and subtraction. We handle these operations step by step. Starting with addition simplifies the expression by combining or removing values, which sets up for a straightforward subtraction afterward.
Remember, when you add a negative number, you're effectively subtracting. And when you subtract, ensure you recognize whether you're taking away a larger number. This will affect if the result is negative or positive.

Negative Numbers

Negative numbers can be a bit tricky at first, but they're fascinating! Simply put, negative numbers are numbers less than zero. They are represented with a minus sign (−). Here are some key points to understand:

• **Negative numbers** are used to express a loss, decrease, or below zero situations, like temperatures or debts.
• When you add a negative number to a positive number, you actually subtract the negative. For example, adding -3 to 10 is the same as subtracting 3 from 10.
• Subtracting a negative number is like adding the absolute value of that number. However, in our original exercise, we didn't subtract negative numbers, but knowing this can help in other contexts!

In our expression of \(20 + (-17) - 8\), \(-17\) is the negative number. We treat it differently because of its sign. It influences whether we are adding or subtracting more significantly than positive numbers do.

Order of Operations

The order of operations is like a set of rules that tell us the correct sequence to evaluate mathematical expressions. This is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Here's how it applies:

• Do operations inside **parentheses** first. For our expression, that applied to \(20+(-17)\), but there were no parentheses to rearrange.
• Since there are no exponents or multiplication to consider, we move to **addition and subtraction**. They are done from left to right.
• Addition or subtraction comes into play in our expression, \(20+(-17)-8\). First, evaluate \(20+(-17)\) and then subtract \(8\).

By following the order of operations, we ensure that everyone interprets the expression in the same way and arrives at the correct result. It's crucial in solving complex expressions without making errors.