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Chapter 2: Problem 343

In the following exercises, simplify. $$ (30+6) \div 2 $$

Short Answer

Expert verified
18

Step by step solution

01

- Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: \(30 + 6\). This gives: \(36\).
02

- Perform the Division

Next, divide the simplified result by 2: \(36 \div 2\). This calculates to: \(18\).

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Key Concepts

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

Order of Operations
When simplifying expressions, '**Order of Operations**' is vital to get the correct result. The commonly used acronym for remembering the Order of Operations is **PEMDAS**:

  • **P** - Parentheses
  • **E** - Exponents
  • **M** - Multiplication
  • **D** - Division
  • **A** - Addition
  • **S** - Subtraction
This tells us to handle calculations inside parentheses first, then exponents, followed by multiplication and division from left to right, and finally, addition and subtraction from left to right.
For example, in the expression \((30+6) \div 2\), you follow steps as indicated in **PEMDAS**, leading us to first deal with the sum inside the parentheses before moving on to division.
Parentheses
Parentheses play a crucial role in shaping the order in which operations are executed. Expressions within parentheses take the highest priority.
For instance, in the provided exercise, the expression '**(30+6) \div 2**' has a part enclosed in parentheses,
so you first perform the addition operation inside the parentheses.
Calculating this first gives us:
\[30 + 6 = 36\]
Once the parentheses are simplified, you remove them, and the expression changes to '**36 \div 2**'. By doing this,
we ensure that we're simplifying in the correct order and maintaining mathematical accuracy.
Division
After handling all parentheses in an expression, the next step in 'PEMDAS' is **Multiplication and Division**.
These two operations are performed from left to right as they appear in the expression.
In our exercise, after simplifying inside the parentheses, the expression is '**36 \div 2**'.
Now, we handle the division operation:
\[36 \div 2 = 18\]
This leads us to the final simplified form of the given expression: 18.
By understanding and following the order of operations, including accurate handling of parentheses and divisions,
we ensure reliability in reaching the correct answer.

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