Today we’re going to learn about a fundamental concept in algebra called PEMDAS. This is a mnemonic that helps us remember the order in which we should perform operations in a mathematical expression. So why is it important? Without a standardized order of operations, a single math problem could have many different answers. PEMDAS gives us a consistent framework for solving math problems.
What Does PEMDAS Stand For?
PEMDAS stands for:
- Parentheses
- Exponents (Powers and Roots, etc.)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
How Do You Use PEMDAS?
Let’s break it down with an example:
Example: Solve the expression 8 + 2 × (15 ÷ 3) – 5²
- First, we solve any operations inside parentheses:
15 ÷ 3 = 5
Now our expression is 8 + 2 × 5 – 5² - Next, we tackle the exponents:
5² = 25
The expression simplifies to 8 + 2 × 5 – 25 - Then we perform multiplication and division, from left to right:
2 × 5 = 10
And the expression becomes 8 + 10 – 25 - Lastly, we handle addition and subtraction, from left to right:
8 + 10 = 18
18 – 25 = -7
So the final answer is -7.
Frequently Asked Questions
Do Multiplication and Division have the same priority?
Yes, they do. When you have both multiplication and division in a problem, you perform them from left to right. The same goes for addition and subtraction.
What if there are multiple sets of Parentheses?
If there are multiple sets of parentheses, you work from the innermost set outwards.
Can you give another example?
Of course! Let’s solve 4 + (3² – (2+1)) × 2:
- Solve the innermost parentheses first: (2+1) = 3
- Replace and solve the next set: 3² – 3 = 9 – 3 = 6
- Now, multiply by 2: 6 × 2 = 12
- Finally, add 4: 4 + 12 = 16
So the answer is 16.
I hope this lesson on PEMDAS has been helpful. Remember to always follow the order of operations to get the correct answer in your math problems!
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