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Chapter 0: Problem 35

For exercises 1-80, evaluate. $$ 6+5 \cdot 0 $$

Short Answer

Expert verified
6

Step by step solution

01

- Understand the Order of Operations

Identify the operations in the expression, which are addition and multiplication. According to the order of operations (PEMDAS/BODMAS), multiplication should be performed before addition.
02

- Perform the Multiplication

Evaluate the multiplication part of the expression first: \(5 \times 0 = 0\)
03

- Perform the Addition

Now add the result of the multiplication to the other number in the expression: \(6 + 0 = 6\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations: PEMDAS
To correctly solve mathematical expressions, it's crucial to use the rule of Order of Operations, often remembered by the acronym PEMDAS.
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
This rule defines the sequence in which operations need to be performed to ensure accurate results.
For example, in the expression \(6 + 5 \cdot 0\), you must first handle any operations of multiplication before moving on to addition. This avoids common errors, leading you to the correct answer.
Multiplication in Order of Operations
Multiplication is a fundamental operation in mathematics and always has to be addressed before addition and subtraction according to PEMDAS.
Consider the given exercise: \(6 + 5 \cdot 0\). According to the order of operations, you perform the multiplication first. Multiplying 5 by 0 gives us 0.
Thus, the expression simplifies to \(6 + 0\).
Remember, regardless of the numbers, any number multiplied by zero results in zero. This can significantly reduce the complexity of an expression almost immediately.
Addition after Multiplication
Once multiplication is handled, you proceed to addition.
Looking again at our simplified expression \(6 + 0\), we now need to add these numbers together.
This is straightforward: adding zero to any number leaves the number unchanged.
Hence, \(6 + 0\) equals 6.
It's essential to follow the order of operations to simplify expressions correctly.
Always perform multiplication before addition to avoid mistakes and reach the accurate answer.

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