Order of Operations
Basics on the topic Order of Operations
Order of Operations – Introduction
Exploring mathematics can sometimes feel like navigating a vast ocean of numbers and equations. To journey through these waters, one essential tool is understanding the Order of Operations. Just as a ship uses a compass to reach its destination, we use the Order of Operations to find the correct solution to mathematical problems.
Understanding the Order of Operations – Explanation
The Order of Operations is the agreed-upon standard that dictates the correct sequence for calculating expressions, avoiding ambiguity and ensuring consistency across all mathematical calculations.
Exploring mathematics involves understanding essential concepts such as the Order of Operations. We often liken this to navigating through complex pathways, where each step must follow a specific sequence to reach the correct solution. Let's consider the acronym GEMS to simplify the Order of Operations:
| Step | Operation Type | Description |
|---|---|---|
| 1 | Grouping Symbols (G) | Complete all operations inside grouping symbols first. |
| 2 | Exponents (E) | Calculate powers and roots next. |
| 3 | Multiply/Divide (M) | Perform multiplication and division, from left to right. |
| 4 | Subtract/Add (S) | Finally, handle subtraction and addition, from left to right. |
Order of Operations – Example
Let's solve an example problem to demonstrate the Order of Operations using the GEMS method.
Calculate: $5 + 2 \times (3^{2} - 1)$
Here's how it breaks down using a table:
| Step | Description | Calculation |
|---|---|---|
| Grouping Symbols | Solve the expression within the parentheses first. | $3^{2} - 1$ becomes $9 - 1 = 8$ |
| Exponents | There are no more exponents to calculate after the first. | - |
| Multiply/Divide | Carry out the multiplication next. | $2 \times 8 = 16$ |
| Subtract/Add | Finally, perform the addition. | $5 + 16 = 21$ |
So, $5 + 2 \times (3^{2} - 1) = 21$.
Order of Operations – Guided Practice
Now, let's solve another problem step-by-step:
Calculate: $6 \times (2 + 4) \div 3^{2}$
Try solving the following expression by applying the GEMS Order of Operations:
Calculate: $4^{2} - 3 \times (8 \div 2 + 5)$
Order of Operations – Summary
Key Learnings from this Text:
- The Order of Operations is crucial for solving math problems correctly.
- GEMS is the acronym used to remember the order: Grouping symbols, Exponents, Multiply/Divide, and Subtract/Add.
- Operations inside grouping symbols always come first, followed by exponents.
- Multiplication and division are performed from left to right, as are subtraction and addition.
- Following this order ensures that everyone arrives at the same correct answer.
To strengthen your understanding and become proficient at math problems, explore our interactive practice problems, videos, and printable worksheets!
Order of Operations – Frequently Asked Questions
Transcript Order of Operations
"The Snackmaster Pro can do it all! It can add vegetables to the juicer, divide the fruit between the dehydrator and smoothie maker, multiply the number of ingredients, AND it can take out any vegetables you don't like!" "Healthy snacks, activate!" "Well, um, that's not what I was expecting. I'll just do this manually by solving the order of operations on this exclusive LIVE stream! " Order of Operations The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. An expression is a sentence with a minimum of two numbers or variables and at least one math operation. When we evaluate an expression, we use given numbers to create an equation, that we can then find the value of. The math operations could be addition, subtraction, multiplication, or division. We can use the acronym GEMS to solve expressions from LEFT to RIGHT. The stands for subtract, and add, and we ALWAYS solve from left to right. You may not see all these operations in one expression, and following the order of operations is important because if you don't, you may get the wrong answer. Let's solve two plus eleven times four. When using GEMS, we start from left to right. Are there any parenthesis or exponents? (...) No, so we move on to multiplying eleven times four FIRST, which equals forty-four. Since there is no multiplication or division, what operation do we perform next? (...) We add two plus forty-four which equals forty-six. Let's see what happens when we don't follow the order of operations here and just solve from left to right. IF we add two and eleven to get thirteen, and multiply thirteen times four we get fifty-two, which is the WRONG answer. This is why it's important to follow the order of operations. Let's help Penny solve THIS expression. Looking from left to right, do you see grouping symbols? (...) Yes, so solve seventeen minus six FIRST to get eleven. Are there any exponents? (...) No, so move on to multiplying three times five to get fifteen. What is the next step? (...) Since there is no division, we add fifteen plus eleven. What is the sum of fifteen and eleven? (...) Twenty-six. Penny has another snack combination represented by THIS expression. Pause the video to try solving on your own and press play when you're ready. Since there are no grouping symbols or exponents, we divide twelve and two to get six. Then, add six plus eight to get fourteen. Last, subtract one from fourteen which equals thirteen. While Penny wraps up, let's summarize. The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can use the acronym GEMS to solve expressions from LEFT to RIGHT. Following the order of operations is important because if you don't, you may get the wrong answer. "Mmmm delicious!"
