Problem 64 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ -1(4+2) $$

Step-by-Step Solution

Answer

Answer: The value of the expression is \(-6\).

Step 1: Evaluate expression inside parenthesis

The expression inside the parenthesis is \(4 + 2\). To find the sum of these two numbers, simply add them together: \(4 + 2 = 6\). The expression now becomes: \(-1(6)\).

Step 2: Perform multiplication

Now, we have a multiplication operation between \(-1\) and \(6\). To perform this multiplication, simply multiply the numbers together: \(-1 \times 6 = -6\). So, the value of the given expression \(-1(4+2)\) is \(-6\).

Key Concepts

Understanding Parentheses

Parentheses are an important part of math, acting like containers in our equations. They tell us which part of an expression to calculate first. When you see something wrapped in parentheses, like \((4+2)\), it means you need to find the result of this part before doing anything else.

This is known as "order of operations," often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). It helps everyone do math in the same way and get the correct result.

So, when looking at our original expression \(-1(4+2)\), we start by solving inside the parentheses.

Addition Inside Parentheses

Next, we'll focus on what happens inside the parentheses: \(4 + 2\). Addition is about combining numbers to get a total sum.

Here's how it works:

• Take the first number, which is 4.
• Add the second number, which is 2.

When you put them together, you get \(4 + 2 = 6\).

This gives us the new expression: \(-1(6)\). Now, we move on to the next step of multiplication.

Multiplication with Negative Numbers

Multiplication tells us how many times to add a number to itself. In the expression \(-1(6)\), we need to multiply \(-1\) by \(6\).

Here's how multiplication works with negative numbers:

• A positive times a positive is positive.
• A negative times a positive is negative.
• Two negatives make a positive.

Since we're multiplying a negative by a positive: \(-1 \times 6 = -6\).

This means we're effectively adding \(-6\) to zero. That's how we arrive at the final answer of \(-6\).

Working with Negative Numbers

Negative numbers represent values less than zero, like owning a debt instead of having savings. When you see a negative sign in math, it's an indicator of direction, showing we are on the opposite side of a number line.

Understanding negative numbers can be tricky at first. Here's a quick way to think about them:

• Adding a negative is like subtraction.
• Subtracting a negative is like addition.
• Multiplying by a negative flips the sign.

In our final step, multiplying \(-1\) by \(6\) flips the positive 6 into \(-6\), completing the problem.