Problem 50 - Beginning and Intermediate Algebra

Question

Add See Examples \(\ell\) through 7 . $$ 8+(-2)+7 $$

Step-by-Step Solution

Answer

The sum of the expression is 13.

Step 1: Understand the Problem

The expression given is \(8 + (-2) + 7\). We need to find the sum of these three numbers.

Step 2: Simplify Signs

The second term is \(-2\), which means we are subtracting 2 from the sum. The expression can also be written as \(8 - 2 + 7\).

Step 3: Perform the First Operation

Start by solving \(8 - 2\). This is a simple subtraction: \(8 - 2 = 6\).

Step 4: Add the Remaining Number

Now take the result from Step 3, which is 6, and add the last number: \(6 + 7 = 13\).

Key Concepts

Subtraction

Subtraction is one of the core arithmetic operations, often introduced as "taking away". In mathematics, subtraction helps us find the difference between numbers. For young learners, think of subtraction as counting backwards. When you see a problem like \[8 - 2\]you start at 8 and count 2 steps back.

• Start at the first number: 8
• Move back 2 steps. Count backwards: 7 and then 6.

The result is 6. So, \[8 - 2 = 6\].
In arithmetic expressions, negative signs sometimes indicate subtraction. In the problem\[8 + (-2) + 7\],the \(-2\) acts as a subtraction: \[8 - 2\].To master subtraction, always remember the idea of moving backwards.

Simplifying Expressions

Simplifying expressions makes mathematics easier to understand. It's like tidying up your workspace so you can see what you're working with. In arithmetic, this often means combining like terms or simplifying signs. With our expression \[8 + (-2) + 7\], we first identify that \(-2\),which can make it easier to view as \[8 - 2 + 7\].
The goal is to express the problem in an easy-to-solve form. When simplifying:

• Look for negative signs preceding numbers. These may indicate subtraction.
• Rearrange subtraction to make it clearer, such as changing \[+ (-2)\] to \[- 2\].
• Focus on order to solve the equation step-by-step, maintaining clear sight of the operations.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics. They include addition, subtraction, multiplication, and division. Each operation has rules that guide how to solve problems. Understanding and applying these rules is key to solving arithmetic problems effectively.
For instance, in the expression \[8 + (-2) + 7\]:

• First, perform subtraction using \[8 - 2\] to get 6.
• Next, add the remaining number \[6 + 7\], resulting in \[13\].

The goal is to perform one operation at a time. Start with subtraction and then move to addition step-by-step. Consistency in following the steps ensures accuracy. Remember: arithmetic operations guide the path to finding the right answer.