Question

Evaluate each expression. $$ -6+4 \cdot 3 $$

Short answer

6

Step-by-step solution

Apply Order of Operations

Recall the order of operations. According to PEMDAS/BODMAS, we must perform multiplication before addition and subtraction.

Perform Multiplication

Multiply 4 by 3. \[ 4 \times 3 = 12 \]

Substitute and Simplify

Replace the multiplication result in the original expression, then simplify: \[ -6 + 12 \]

Perform Addition

Add -6 and 12: \[ -6 + 12 = 6 \]

Key concepts

Understanding PEMDAS

PEMDAS is an acronym to help remember the order of operations in mathematics. It stands for: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This order is crucial because it tells us the sequence to solve a mathematical expression. By following PEMDAS, we avoid errors and get the correct solution every time.

• First, solve expressions inside parentheses.
• Second, resolve exponents.
• Third, perform multiplication and division as they appear from left to right.
• Finally, perform addition and subtraction from left to right.

Let's look at the exercise: -6 + 4 ⋅ 3. According to PEMDAS, we must first handle the multiplication (4 ⋅ 3) before performing the addition.

Mastering Multiplication

Multiplication is one of the basic operations in arithmetic. It combines groups of equal size. For example, 4 multiplied by 3 (4 ⋅ 3) means we have 4 groups of 3. Multiplication is done after anything in parentheses and any exponents according to PEMDAS.
Let's go through the exercise step-by-step:

• In -6 + 4 ⋅ 3, identify the multiplication part first: 4 ⋅ 3.
• Calculate 4 ⋅ 3 = 12.

The expression now becomes -6 + 12 after we’ve handled the multiplication. We'll continue simplifying this in the next step.

Simplifying with Addition

Addition is one of the core arithmetic operations, bringing zero or more numbers together to form a sum. After multiplication, we handle addition following the order of operations.
From our modified expression -6 + 12:

• The expression is now reduced to two terms needing addition.
• Since we're adding a negative (-6) to a positive (12), think of it as moving left from 12 on a number line.
• -6 + 12 = 6. This gives us our final answer.

Therefore, the simpler the steps, the easier it is to find the correct answer.