Order Of Operations: Calculate Math Expressions

by TextBrain Team 48 views

Hey guys! Let's dive into the fascinating world of math and tackle some expressions using the correct order of operations. It's super important to follow the right steps to get the correct answers. So, grab your pencils, and let's get started!

Understanding Order of Operations

Before we jump into the calculations, let's quickly recap the order of operations. You might have heard of the acronym PEMDAS or BODMAS, which helps us remember the correct sequence. It stands for:

  • Parentheses (or Brackets)
  • Exponents (or Orders)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Following this order ensures that we solve mathematical expressions consistently and accurately. Ignoring this order can lead to completely wrong results, and we definitely don't want that!

Calculating 186 - 19 x 5

Let's start with our first expression: 186 - 19 x 5. According to the order of operations, we need to perform multiplication before subtraction.

So, we begin by multiplying 19 by 5.

Multiplication First: 19 x 5 = 95

Now, we substitute this result back into our expression:

Subtraction: 186 - 95 = 91

Therefore, the answer to 186 - 19 x 5 is 91. See? Easy peasy when you follow the order!

In this first problem, the key takeaway is to prioritize multiplication before subtraction. Many people might be tempted to subtract first, but that would lead to the wrong answer. By sticking to PEMDAS/BODMAS, we ensure we're on the right track. Remember, multiplication and division are like best friends; they always come before addition and subtraction.

To solidify your understanding, try to think of real-life scenarios where this order matters. For example, if you're calculating the total cost of items with a discount, you'd multiply the discount percentage by the original price before subtracting it. Order matters in everyday calculations, too!

Calculating 56 - 3 x 9 + 36 : 4

Next up, we have a slightly more complex expression: 56 - 3 x 9 + 36 : 4. This one involves multiplication, division, subtraction, and addition. But don't worry, we'll break it down step-by-step!

Following the order of operations, we tackle multiplication and division first, working from left to right.

Multiplication: 3 x 9 = 27

Division: 36 : 4 = 9

Now, let's rewrite our expression with these results:

56 - 27 + 9

We are left with subtraction and addition. Again, we work from left to right.

Subtraction: 56 - 27 = 29

Addition: 29 + 9 = 38

So, the answer to 56 - 3 x 9 + 36 : 4 is 38. Awesome job!

In this problem, we encountered both multiplication and division. The critical point here is to perform these operations from left to right. It's a common mistake to get confused and perform division before multiplication (or vice versa) just because D comes before M in PEMDAS/BODMAS. Remember, they're equals in the order of operations!

Think of it like reading a sentence – you read from left to right. Similarly, when you have multiplication and division together, you tackle them in the order they appear. This ensures you don't accidentally flip the operations and arrive at a different answer. Practice makes perfect, so keep working on these types of expressions to master the concept.

Calculating 30 - 24 : 3 x (72 : 9 - 2 x 4) : 8 x 9

Alright, let's move on to our final and most challenging expression: 30 - 24 : 3 x (72 : 9 - 2 x 4) : 8 x 9. This expression has it all – parentheses, multiplication, division, subtraction... It looks intimidating, but we'll conquer it using our trusty order of operations!

The first step is to deal with the parentheses. Inside the parentheses, we have 72 : 9 - 2 x 4. We need to apply the order of operations within the parentheses as well.

Inside Parentheses:

  • Division: 72 : 9 = 8
  • Multiplication: 2 x 4 = 8

Now we have 8 - 8 inside the parentheses.

Parentheses (continued):

  • Subtraction: 8 - 8 = 0

Our expression now looks like this: 30 - 24 : 3 x 0 : 8 x 9

Next, we perform multiplication and division from left to right.

Multiplication and Division (left to right):

  • Division: 24 : 3 = 8

Now the expression is: 30 - 8 x 0 : 8 x 9

  • Multiplication: 8 x 0 = 0

The expression becomes: 30 - 0 : 8 x 9

  • Division: 0 : 8 = 0

Now we have: 30 - 0 x 9

  • Multiplication: 0 x 9 = 0

The final expression is: 30 - 0

Finally, we perform the subtraction.

Subtraction:

  • 30 - 0 = 30

Therefore, the answer to 30 - 24 : 3 x (72 : 9 - 2 x 4) : 8 x 9 is 30. Phew! That was a workout for our brains!

This problem highlighted the importance of tackling parentheses first and then methodically working through multiplication and division from left to right. The presence of zero in the expression also showed us how multiplication and division involving zero can simplify things. Remember, anything multiplied by zero is zero, and zero divided by anything (except zero) is also zero.

Don't get discouraged if you found this problem challenging. These complex expressions are like puzzles, and with practice, you'll become a master puzzle solver! Break down the problem into smaller steps, focus on one operation at a time, and always keep PEMDAS/BODMAS in mind.

Tips for Mastering Order of Operations

To become a pro at solving these kinds of expressions, here are a few tips:

  1. Memorize PEMDAS/BODMAS: This acronym is your best friend. Write it down if you need to, and refer to it often.
  2. Practice Regularly: The more you practice, the more natural the order of operations will become. Try solving different types of expressions with varying levels of complexity.
  3. Break It Down: For complex expressions, break them down into smaller, manageable steps. Focus on solving one operation at a time.
  4. Double-Check Your Work: It's always a good idea to double-check your calculations to avoid simple errors.
  5. Use Parentheses Wisely: If you're unsure about the order, use parentheses to clarify which operations should be performed first.
  6. Online Resources: There are tons of fantastic online resources, including websites and apps, that offer practice problems and explanations of the order of operations.
  7. Ask for Help: If you're struggling, don't hesitate to ask your teacher, a friend, or a family member for help. Math is a team sport sometimes!

Conclusion

So, there you have it, guys! We've successfully calculated three different mathematical expressions by following the order of operations. Remember, PEMDAS/BODMAS is your guide to navigating the world of mathematical expressions. With a little practice and patience, you'll become a whiz at solving even the most complex equations.

Keep practicing, keep exploring, and most importantly, keep having fun with math! Until next time, happy calculating! 🚀