Problem 43 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ 3(4-6) $$

Step-by-Step Solution

Answer

The value of \(3(4-6)\) is \(-6\).

Step 1: Understand the Expression

The given mathematical expression is \(3(4-6)\). This expression involves multiplication and subtraction. It is important to follow the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 2: Solve Inside the Parentheses

According to the order of operations, solve the expression inside the parentheses first: \(4 - 6\). This simplifies to \(-2\). Now the expression is \(3 \times (-2)\).

Step 3: Perform the Multiplication

Multiply the simplified result from the parentheses by the number outside the parentheses: \(3 \times (-2)\). The result of this multiplication is \(-6\).

Step 4: Check Using Calculator

Use a calculator to confirm the arithmetic. Enter \(3 \times (4-6)\) into the calculator, which should give you a result of \(-6\).

Key Concepts

PEMDAS

Are mathematical expressions sometimes overwhelming? The good news is there's a handy rule to help, called PEMDAS. This stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This rule tells you the order to solve different parts of a math problem.

Think of PEMDAS as a checklist:

• First, solve anything inside Parentheses.
• Next, look for Exponents, like squares or cubes, and solve those.
• After that, handle any Multiplication and Division, working from left to right.
• Finally, do any Addition and Subtraction, also from left to right.

Using PEMDAS gives you the right answer every time. It’s especially important in complex math problems, where skipping around might lead to errors. Just remember, by following the PEMDAS order, you're less likely to make mistakes!

Multiplication

Multiplication is not just repeated addition, it's an essential math operation. In our expression, after simplifying the parentheses we have: \(3 \times (-2)\). Here, multiplication does the magic.

When you multiply a positive number by a negative number, your result will be negative. The rule here is simple:

• A positive times a positive gives you a positive.
• A positive times a negative, or vice versa, will result in a negative.
• Negative times negative results in positive.

So, in \(3 \times (-2)\), you multiply 3 by -2, giving \(-6\). Multiplication is powerful and lets you solve tasks quickly, whether it's calculating areas, scaling quantities, or distributing resources.

Subtraction

Subtraction is all about taking one number away from another. It’s one of the first operations we learn and is crucial in solving our earlier expression inside the parentheses: \(4 - 6\).

When you’re subtracting a larger number from a smaller one, you end up with a negative result. Here are some simple pointers to remember:

• Subtracting a smaller number from a bigger number? The result is a regular, positive number.
• A bigger number minus a smaller number becomes negative.
• Subtracting zero doesn't change a number.

In our example, \(4 - 6\) equals \(-2\). This is because 4 is less than 6, thereby resulting in a negative number. Subtraction is everywhere, from finding differences in distances to balancing your checkbook!