Problem 83 - Algebra A Combined Function

Question

Evaluate each expression. \(-3(2-8)\)

Step-by-Step Solution

Answer

The expression evaluates to 18.

Step 1: Solve inside the parenthesis

Inside the expression, there is a calculation within the parenthesis, \(2 - 8\). Solve this operation by subtracting 8 from 2, which equals -6.

Step 2: Multiply by the outside factor

Now, take the result from step 1 which is -6, and multiply it by the factor outside the parenthesis, which is -3. Compute \(-3 \times -6\).

Step 3: Calculate the multiplication

Multiply \(-3\) by \(-6\). The product of two negative numbers is positive, therefore \(-3 \times -6 = 18\).

Key Concepts

Order of Operations

When faced with a mathematical expression, it's crucial to solve it in the correct order. This is known as the "order of operations," and it ensures everyone interprets and solves expressions in the same way. The correct sequence to follow is often remembered using the acronym PEMDAS:

• P - Parentheses
• E - Exponents
• M - Multiplication
• D - Division
• A - Addition
• S - Subtraction

The order is important because performing operations in the wrong sequence can lead to incorrect answers. In our original exercise, we started with what was inside the parentheses first, following the PEMDAS rule clearly.

Multiplication of Integers

Multiplying integers can sometimes be confusing, but it's quite straightforward once you know the rules. It involves simple multiplication, except you also need to take the signs into consideration:

• Multiplying two positive integers gives a positive product.
• Multiplying two negative integers also results in a positive product.
• If one integer is positive and the other is negative, the product will be negative.

In our exercise, solving \(-3 \times -6\) resulted in a positive 18, because both integers were negative.

Negative Numbers

Negative numbers can sometimes be a tricky concept because they are less intuitive than positive numbers. They lie on the left side of zero on the number line, and handling them correctly is crucial in algebraic expressions. One important aspect to remember:

• Adding a negative is like subtracting a positive.
• Subtracting a negative is like adding a positive.
• The product or quotient of two negatives is a positive.

In the original exercise, both -3 and -6 were negative, resulting in a positive 18 when multiplied.

Parentheses in Mathematics

Parentheses are an essential part of algebra and help organize expressions by indicating which operations should be performed first. They can be thought of as a "priority" marker that tells you: "This needs to be handled before anything else!"
Using parentheses, you can alter the default order of operations. For instance, without parentheses, an expression such as 2 - 8 × 3 would first multiply then subtract, but with parentheses as in \(-3(2 - 8)\), you handle the \(2 - 8\) first.
The right use of parentheses is pivotal in tackling algebraic difficulties head-on. In our original exercise, the presence of parentheses meant solving \(2 - 8\) before multiplying by -3.