Solving 1*3 × (14-4×3): (72:12-2*2): A Step-by-Step Guide

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Hey guys! Math can sometimes look intimidating, especially when you're faced with an expression like 13 × (14-4×3): (72:12-22). But don't worry, we're going to break it down step-by-step, making it super easy to understand. This guide will not only give you the answer but also show you exactly how to get there. The options we have are A) 6, B) 12, C) 18, and D) 24. So, let's dive in and figure out which one is correct!

Understanding the Order of Operations

Before we even start crunching numbers, it’s super important to understand the order of operations. Remember the acronym PEMDAS, which stands for:

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

This order is the key to solving any mathematical expression correctly. Ignoring PEMDAS is like trying to build a house without a blueprint – things can get messy quickly! So, keep PEMDAS in mind as we tackle our expression.

Let's Apply PEMDAS to Our Problem

Our expression is: 13 × (14-4×3): (72:12-22)

Following PEMDAS, we'll start with the parentheses. We have two sets of parentheses, so we'll work through each one separately, still keeping PEMDAS in mind within each set.

Step 1: Solve the First Parenthetical Expression (14-4×3)

The first set of parentheses is (14-4×3). Within this, we have subtraction and multiplication. According to PEMDAS, multiplication comes before subtraction.

  • First, multiply: 4 × 3 = 12
  • Now our expression inside the parentheses looks like: (14 - 12)
  • Next, subtract: 14 - 12 = 2

So, the first parenthetical expression (14-4×3) simplifies to 2. Great job! We’re one step closer.

Step 2: Solve the Second Parenthetical Expression (72:12-2*2)

Now let's tackle the second set of parentheses: (72:12-2*2). This one involves division, subtraction, and multiplication. Remember, multiplication and division are on the same level in PEMDAS, so we perform them from left to right.

  • First, divide: 72 : 12 = 6
  • Now our expression inside the parentheses looks like: (6 - 2*2)
  • Next, multiply: 2 * 2 = 4
  • Now it looks like: (6 - 4)
  • Finally, subtract: 6 - 4 = 2

So, the second parenthetical expression (72:12-2*2) also simplifies to 2. Awesome! We’ve handled both sets of parentheses.

Step 3: Rewrite the Simplified Expression

After simplifying the expressions within the parentheses, our original expression now looks much cleaner:

1 * 3 × 2 : 2

This is much easier to manage, right? Now we just have multiplication and division to deal with. Remember, these operations are performed from left to right.

Step 4: Perform Multiplication and Division from Left to Right

We have 1 * 3 × 2 : 2. Let’s go from left to right:

  • First, multiply: 1 * 3 = 3
  • Now our expression is: 3 × 2 : 2
  • Next, multiply: 3 × 2 = 6
  • Now it’s: 6 : 2
  • Finally, divide: 6 : 2 = 3

Wait a minute! We arrived at 3, but that isn't one of the options. Let’s carefully review our steps to ensure we didn’t make a small mistake anywhere. It's always a good idea to double-check your work in math!

Double-Checking Our Steps

Okay, let’s quickly go through each step again:

  1. Parentheses 1: (14 - 4 × 3) = (14 - 12) = 2 – This looks correct.
  2. Parentheses 2: (72 : 12 - 2 * 2) = (6 - 4) = 2 – This also looks right.
  3. Simplified Expression: 1 * 3 × 2 : 2 – Seems good.
  4. Multiplication and Division: 1 * 3 = 3, 3 * 2 = 6, 6 : 2 = 3

Hmm, everything seems to be in order. It appears there might be a discrepancy between our result and the provided options. Our calculation confidently leads us to 3. It's possible there was a typo in the original question or answer choices.

Conclusion: The Correct Solution and What to Do When Answers Don't Match

After carefully following the order of operations (PEMDAS) and double-checking our work, we've determined that the solution to the expression 13 × (14-4×3): (72:12-22) is 3. However, 3 is not one of the options provided (A) 6, B) 12, C) 18, D) 24).

What Should You Do If This Happens on a Test?

If you encounter a situation like this on a test or in an assignment, here’s what I recommend:

  1. Double-Check Your Work: Just like we did, go through your steps again. It’s easy to make a small mistake, and a fresh look can help you catch it.
  2. Review the Question: Make sure you've copied the question correctly and haven't missed any details.
  3. If Still No Match, Choose the Closest Answer: If you’re confident in your solution but it doesn't match the options, pick the answer that's closest to your result. In this case, if 3 were not an option, we'd have a bit of a dilemma, but since it's definitively the correct answer, it highlights a potential issue with the provided choices.
  4. If Possible, Ask for Clarification: If you're in a classroom setting, raise your hand and politely ask your teacher if there might be a mistake in the options. It’s always better to clarify if you’re unsure.
  5. Show Your Work: When you submit your test or assignment, make sure to clearly show your steps. This way, even if the final answer doesn't match the options, the teacher can see your understanding of the process and may award partial credit.

In our case, since we’ve meticulously followed PEMDAS, we are confident in our result of 3. This situation underscores the importance of understanding the process and not just memorizing answers. Math isn't just about getting the right answer; it's about the journey and the logical steps you take to get there. Keep practicing, and you’ll become a math whiz in no time!