Problem 55 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(-10-(-4)(2)\)

Step-by-Step Solution

Answer

-2

Step 1 - Simplify the expression inside the parentheses

First, simplify -10 - (-4)(2)

Step 2 - Multiply the numbers

Multiply (-4) and (2) -10 -( - 4 * 2) -10 -(-8).

Step 3- Subtract the simplified result

To subtract a negative number is the same as adding its positive. Therefore,- 10 - (-8) becomes -10 + 8 = -2

Key Concepts

Integer Operations

Understanding integer operations is crucial in algebra. Integers are whole numbers that can be positive, negative, or zero. When performing operations with integers, it's important to pay attention to the signs. For example, adding a negative number is the same as subtracting its absolute value, and subtracting a negative number is the same as adding its absolute value.
Let's look at the given problem: -10 - (-4)(2). Here we see both subtraction and multiplication of integers.

• Multiplication: -4 multiplied by 2 is -8. The multiplication rules for integers are: a positive times a positive equals a positive, a positive times a negative equals a negative, and a negative times a negative equals a positive.
• Subtraction: When we subtract -8, it is the same as adding 8. So, -10 - (-8) simplifies to -10 + 8.

Once you understand these rules, handling integer operations becomes much easier.

Order of Operations

The Order of Operations is a fundamental concept in mathematics. It tells us the sequence in which we should perform operations in a given problem. The standard order is: Parentheses first, then Exponents (or roots), followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). This rule is often remembered by the acronym PEMDAS.
In the problem -10 - (-4)(2), we first deal with the expression inside the parentheses. This is crucial because ignoring the order can result in the wrong answer. After simplifying inside the parentheses, we move on to multiplication before finally handling subtraction.
Applying PEMDAS correctly ensures that we get the correct solution systematically.

Simplification

Simplification is about breaking down a complex expression into simpler, more manageable parts. This makes it easier to solve. In algebra, we often need to simplify expressions before we can find the answer.
Let's simplify the expression step by step:

• First, identify and simplify any operations inside parentheses: In the problem, -4 and 2 are inside parentheses, which results in -8 when multiplied.
• Next, address any multiplication or division: We've already handled the multiplication of -4 and 2, which simplified to -8.
• Finally, perform any addition or subtraction: -10 - (-8) becomes -10 + 8, because subtracting a negative is the same as adding its positive.

A clear and methodical approach to simplification leads to the correct solution. Understanding these steps will help you tackle more complex problems with confidence.