Problem 16 - Prealgebra

Question

Find the value of each expression. $$12-3 \times 3$$

Step-by-Step Solution

Answer

The value of the expression is 3.

Step 1: Understand the Order of Operations

To solve the expression correctly, you must 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). In this expression, there is multiplication and subtraction involved.

Step 2: Perform the Multiplication First

According to the order of operations, you must first perform the multiplication before doing the subtraction. Calculate the multiplication part of the expression: \(3 \times 3\). This calculation results in 9.

Step 3: Subtract the Result from the Multiplication

Now that you have the result of the multiplication, substitute it back into the expression. Thus, the expression becomes \(12 - 9\). Perform this subtraction to get the final answer.

Step 4: Solve the Final Subtraction

Calculate \(12 - 9\), which equals 3. This is the final result of the original expression.

Key Concepts

Understanding PEMDAS

If you want to solve math problems accurately and efficiently, it's crucial to follow a set of rules. These rules are known as the order of operations, often remembered by the acronym PEMDAS. PEMDAS stands for:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

When you have a problem with more than one operation, these rules tell you which calculation to perform first. Parentheses come first; anything inside them should be calculated right away. Next are exponents, those tiny numbers that show how many times to multiply a number by itself. Following this, you handle multiplication and division.

Here’s an important tip: multiplication and division should be carried out from left to right, whichever comes first in the expression. The same goes for addition and subtraction. Stick to PEMDAS, and you'll always arrive at the correct answer!

Importance of Multiplication

In arithmetic, multiplication is one of the primary operations you must solve as early as possible when following PEMDAS. Multiplication is essentially a faster way of adding. For example, if you wanted to add 3 together three times, you could say it's just 3 multiplied by 3. In our expression, this operation is represented as \(3 \times 3\).

To effectively solve this, start by replacing the multiplication operation in your expression with its result. In this case, \(3 \times 3\) gives us 9. Once you have the result of the multiplication, it simplifies the problem, allowing you to focus on the next steps or operations. Remember, whenever you see multiplication alongside other operations, tackle it before moving on to addition or subtraction.

Mastering Subtraction

Subtraction may seem simple, but doing it correctly in order of operations is vital. It’s the process of taking one number away from another, essentially finding the difference. Subtraction's place in PEMDAS comes after multiplication and division, meaning you'll often handle it later in solving expressions.

Let’s revisit our example. After performing the necessary multiplication, you simplify the original problem to \(12 - 9\). The subtraction here is straightforward: simply take 9 away from 12. Doing this, you get 3 as a result.

• First, complete multiplication or division
• Then, carry out any addition or subtraction, from left to right

Knowing how to perform subtraction correctly after other operations is a must for solving complex expressions accurately!

The Basics of Arithmetic

Arithmetic is the branch of mathematics that deals with numbers and the fundamental operations: addition, subtraction, multiplication, and division. These operations are the building blocks of more advanced mathematics. When tackling expressions, understanding each operation's role is crucial.

Order of operations, or PEMDAS, provides a clear pathway to approaching arithmetic problems. It ensures that calculations are done in the correct sequence, maintaining consistency across different solutions. Each component of arithmetic has its place:

• Multiplication and division typically come before addition and subtraction.
• Subtraction adjusts quantities, finding differences.
• These operations combine to solve problems and reach accurate results.

Arithmetic skills are not only essential for academic success; they're practical skills used in everyday life. By mastering these, you’ll be better equipped to handle various numerical challenges!