Understanding the PEMDAS Rule
When it comes to solving math problems with different operations, it’s important to follow a specific order to get the correct result. The PEMDAS rule provides a clear order of operations. It ensures that even the most complex expressions are solved correctly by following the right order of operations.
What is PEMDAS?
PEMDAS stands for:
- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction
The PEMDAS rule tells us which operations to do first, ensuring that we don’t make mistakes when solving math problems with multiple operations like addition, multiplication, and division.
PEMDAS Rule: Order of Operations
Let’s look at each part of the PEMDAS rule in detail:
Parentheses (P):
Always start with the operations inside parentheses. Parentheses group numbers and operations, and whatever is inside must be solved first.Example:
In the expression (3 + 2) × 5, you solve 3 + 2 = 5, then multiply: 5 × 5 = 25.Exponents (E):
After parentheses, handle any exponents. Exponents include things like squares () or cubes (), which are numbers multiplied by themselves.Example:
In the expression 2^3 + 4, first solve 2^3 = 8, then add: 8 + 4 = 12.Multiplication and Division (MD):
Next, handle multiplication and division, working from left to right. These two operations are equally important, so whichever comes first as you read the expression is solved first.Example:
For 8 ÷ 4 × 3, you first divide: 8 ÷ 4 = 2, then multiply: 2 × 3 = 6.Addition and Subtraction (AS):
Finally, handle addition and subtraction, also working from left to right. Like multiplication and division, addition and subtraction are of equal importance, so solve whichever comes first.Example:
In 15 – 5 + 2, subtract first: 15 – 5 = 10, then add: 10 + 2 = 12.
Example Problems
Let’s apply the PEMDAS rule to some example problems.
Example 1:
Solve (8 + 3) × 2 – 5^2
- Step 1: Solve the parentheses first: 8 + 3 = 11.
- Step 2: Handle the exponent: 5^2 = 25.
- Step 3: Multiply: 11 × 2 = 22.
- Step 4: Subtract: 22 – 25 = -3.
The answer is -3.
Example 2:
Solve 6 + 4 × (9 ÷ 3) – 7
- Step 1: Solve inside the parentheses: 9 ÷ 3 = 3.
- Step 2: Multiply: 4 × 3 = 12.
- Step 3: Add and subtract: 6 + 12 = 18, then 18 – 7 = 11.
The answer is 11.
Why is the PEMDAS Rule Important?
Consider this math problem:
7 + 3 × 2
If you simply go from left to right, you might think:
7 + 3 = 10
10 × 2 = 20
But this is wrong!
According to the PEMDAS rule, multiplication comes before addition. So, the correct way to solve it is:
3 × 2 = 6, then 7 + 6 = 13.
The correct answer is 13, not 20! Following PEMDAS ensures you always get the right answer.
Mastering the PEMDAS rule is key for kids to:
- Solve complex problems accurately: With multiple operations in a problem, PEMDAS ensures they are tackled in the correct order.
- Improve logical thinking: The rule helps students think systematically, breaking down complex expressions into simpler steps.
- Avoid calculation errors: By following PEMDAS, students minimize mistakes and ensure their answers are always correct.
Common Mistakes When Using PEMDAS
Here are a few common mistakes students make when using the PEMDAS rule:
- Not solving parentheses first: Always complete the operations inside parentheses before moving on.
- Skipping exponents: Students sometimes forget to solve exponents early. Make sure to handle them after parentheses but before multiplication or division.
- Confusing the order of operations: Always remember that multiplication and division, as well as addition and subtraction, should be solved from left to right as they appear in the expression.
PEMDAS Practice Problems
Try these on your own, following the PEMDAS rule:
(10 + 5) × 2^2 – 8 ÷ 4 + 7
(12 – 4) × 3 + 18 ÷ 6 – 2^2
Answers:
- 65
- 23
BODMAS and PEMDAS
The difference between BODMAS and PEMDAS lies primarily in the terminology used to describe the order of operations, though both represent the same underlying principles. BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction, while PEMDAS represents Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
BODMAS emphasizes “Brackets” and “Orders,” while PEMDAS emphasizes “Parentheses” and “Exponents.” Both acronyms serve the same purpose of clarifying the order of operations in mathematical expressions, ensuring consistency and accuracy in calculations, regardless of the terminology used.
FAQs on PEMDAS
Most modern calculators automatically follow the PEMDAS rule. However, it’s important to input the expression correctly. For complex expressions, it’s a good idea to use parentheses to ensure that the operations are performed in the correct order.
Like multiplication and division, addition and subtraction are performed from left to right. If subtraction appears first when reading the expression from left to right, you solve it before addition. For example, in 10−3+2, subtract first: 10−3=7, then add: 7+2=9.
If you’re confused, refer back to the PEMDAS rule and always start with Parentheses, then Exponents, followed by Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. Solving step by step, while checking each operation, can help clear up any confusion.