Question

Evaluate each expression. $$ 18-5 \cdot 2 $$

Short answer

8

Step-by-step solution

Identify the Order of Operations

In mathematics, expressions are evaluated according to 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)).

Perform Multiplication

According to the order of operations, multiplication is performed before subtraction. Evaluate the expression inside the expression: \[5 \cdot 2 = 10 \]

Perform Subtraction

Now subtract the result of the multiplication from 18: \[18 - 10 = 8\]

Key concepts

PEMDAS

When solving math problems, it's important to follow the correct order of operations. This is where the acronym PEMDAS comes in handy. PEMDAS stands for:

* Parentheses
* Exponents
* Multiplication and Division (left to right)
* Addition and Subtraction (left to right)

This means you should first solve expressions inside parentheses, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right. Following these rules ensures that everyone solves the problem the same way and gets the same result.

Multiplication

In the given math problem, \(18 - 5 \cdot 2\), we must perform multiplication before subtraction, according to the PEMDAS rule. This is because multiplication comes before subtraction in the order of operations.

To perform the multiplication, we calculate: \[5 \cdot 2 = 10 \]

This step is crucial because if we skip it, or perform subtraction first, we will end up with an incorrect result. Remember, multiplication must always be completed before moving on to addition or subtraction in an expression. Always look out for operations in the expression and apply this rule as needed.

Subtraction

After completing the multiplication in the expression, it's time to perform the subtraction. We are left with:

\[18 - 10 = 8\]

Here, 18 is the initial number, and we subtract 10, which is the result of our earlier multiplication.

Subtraction is usually one of the final steps in the order of operations unless addition is also present. Just like with multiplication, it's essential to follow PEMDAS to determine when subtraction should be performed. It ensures that the math problem is correctly solved and avoids any errors. Always double-check to make sure all other operations that come before subtraction have been handled properly.