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Chapter 1: Problem 81

Evaluate the given expression. Remember to follow the order of operations. $$15+12 \div 6-3$$

Short Answer

Expert verified
The value of the expression is 14.

Step by step solution

01

- Identify the order of operations

The order of operations can be remembered using the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
02

- Perform division first

According to PEMDAS, division comes before addition and subtraction. So, evaluate the division part first: \(12 \div 6 = 2\).
03

- Substitute back into the expression

After performing the division, substitute the result back into the expression: \(15 + 2 - 3\).
04

- Perform addition

Next, perform the addition: \(15 + 2 = 17\).
05

- Perform subtraction

Lastly, carry out the subtraction: \(17 - 3 = 14\).

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Key Concepts

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

Understanding PEMDAS
To solve mathematical expressions correctly, we use the order of operations. This order can be remembered with the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The order guides us on which operations to perform first to correctly evaluate expressions.

For instance, in the expression given in the exercise, identifying PEMDAS helps us know that we must handle division before doing any addition or subtraction.
Division in the Order of Operations
Division is a crucial part of the order of operations and comes before addition and subtraction when no parentheses or exponents are involved.

In our example \(15 + 12 \div 6 - 3\), according to PEMDAS, we first deal with the division part. Evaluating the division: \(12 \div 6 = 2\), we get the value for the division operation first. This new value then needs to be used in place of the original division in the next steps.
Performing Addition
Once we have completed the division, we move on to addition. Addition is straightforward within the order of operations: it comes after dealing with any parentheses, exponents, multiplication, and division.

After substituting the result of the division back into the expression, we have: \(15 + 2 - 3\). We then perform the addition: \(15 + 2 = 17\). This result simplifies our expression further, leaving us with the next step.
Performing Subtraction
The final step in evaluating our expression, according to PEMDAS, is subtraction. Once addition is handled, we look at the remaining expression: \(17 - 3\). Subtraction is the last operation we perform.

Evaluating this subtraction gives us: \(17 - 3 = 14\). And that is our final answer.

Remember: always follow the order of operations to solve any mathematical expressions accurately.

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