Problem 63
Question
\(14+8 \div 2\)
Step-by-Step Solution
Verified Answer
The result is 18.
1Step 1: Identify the Operations
The given expression is \(14 + 8 \div 2\). It contains addition and division operations.
2Step 2: Apply the Order of Operations (PEMDAS/BODMAS)
According to the order of operations, division should be performed before addition.
3Step 3: Perform the Division
Calculate \(8 \div 2\). The result is 4.
4Step 4: Perform the Addition
Now add the result of the division to 14: \(14 + 4\). The result is 18.
Key Concepts
Understanding PEMDASThe Role of Division in PEMDASSimplifying with Addition
Understanding PEMDAS
To solve mathematical expressions correctly, you need to follow the PEMDAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It's a guideline to ensure that everyone solves the expression the same way.
For example, in the expression 14 + 8 ÷ 2, according to PEMDAS, you must perform the division first before doing the addition.
This rule is crucial because performing operations out of order can lead to incorrect results.
For example, in the expression 14 + 8 ÷ 2, according to PEMDAS, you must perform the division first before doing the addition.
This rule is crucial because performing operations out of order can lead to incorrect results.
The Role of Division in PEMDAS
In PEMDAS, division takes priority over addition and subtraction, just like multiplication. This is because division and multiplication are considered higher-order operations compared to addition and subtraction.
When you encounter an expression like 14 + 8 ÷ 2, always perform the division first. So you start by computing 8 ÷ 2. This operation simplifies the expression to 14 + 4.
Following this rule ensures that the computations are consistent and accurate.
When you encounter an expression like 14 + 8 ÷ 2, always perform the division first. So you start by computing 8 ÷ 2. This operation simplifies the expression to 14 + 4.
Following this rule ensures that the computations are consistent and accurate.
Simplifying with Addition
Once you have handled division or multiplication, you move on to the lower-priority operations such as addition and subtraction, as per PEMDAS.
In our example, after completing the division (8 ÷ 2 = 4), you're left with a simpler expression: 14 + 4. Now, you can easily complete this final addition step.
The result is 18. This final step is straightforward but crucial, as it finalizes the simplified result of the initial complex expression.
In our example, after completing the division (8 ÷ 2 = 4), you're left with a simpler expression: 14 + 4. Now, you can easily complete this final addition step.
The result is 18. This final step is straightforward but crucial, as it finalizes the simplified result of the initial complex expression.
Other exercises in this chapter
Problem 63
The sales tax rate in a state is \(6 \%\). Find the sales tax on a purchase of \(\$ 750\).
View solution Problem 63
\(3(2 x+1)-(4 x-9)\)
View solution Problem 64
\(\sqrt[3]{-1000}\)
View solution Problem 64
The sales tax rate in a state is \(8 \%\). Find the sales tax on a purchase of \(\$ 550\).
View solution