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Chapter 2: Problem 443

In the following exercises, simplify, using the order of operations. $$ (8+4) \div 3+1 $$

Short Answer

Expert verified
The simplified result is 5.

Step by step solution

01

- Simplify Inside Parentheses

First, perform the operation inside the parentheses. Calculate \(8 + 4\) to get 12. Now the expression is: \[ 12 \div 3 + 1 \]
02

- Division

Next, perform the division operation. Calculate \(12 \div 3\) to get 4. Now the expression is: \[ 4 + 1 \]
03

- Addition

Lastly, perform the addition operation. Calculate \(4 + 1\) to get 5.

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Key Concepts

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

Simplifying Expressions
When you simplify expressions, the goal is to make them easier to work with. Simplifying involves combining like terms and using the order of operations correctly. In our example, the expression is \((8 + 4) \div 3 + 1\). Following the order of operations (parentheses first, then division, and finally addition), we simplify step by step. Understanding each of these operations helps to get the right solution. Remembering terms like PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) can be helpful.
Parentheses
Parentheses are used in mathematics to indicate which operations should be completed first. They take priority over other operations. In our example \((8 + 4) \div 3 + 1\), we first handle the parentheses by adding 8 and 4. This simplifies to 12. Now, the expression becomes \(12 \div 3 + 1\). Parentheses help group parts of an expression, ensuring that calculations are carried out in the correct order to get the right result.
Division
After we simplify what's inside the parentheses, we move to the next operation: division. In our simplified expression \(12 \div 3 + 1\), we need to divide 12 by 3. This operation comes before addition according to the order of operations. Carrying out the division gives us 4. So, the expression now looks like \(4 + 1\). Division splits a number into equal parts, and getting this step right is essential for a correct final answer.
Addition
The final step in our problem is addition. With the expression simplified to \(4 + 1\), we simply add the two numbers. This equals 5. Addition is the process of combining numbers to get a total. In this example, it is the last step after handling parentheses and division. Following these steps correctly ensures we get the right solution: 5.

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