Solve: (6/2)^2 + 7 * 2 | Math Made Easy

Nov 12, 2025 by Andrew McMorgan 40 views

$Work out $\left(\frac{6}{2}\right)^2+7 \times 2$$

Hey there, math enthusiasts! Let's break down this equation together, step by step, making sure everyone understands the process. It might look intimidating at first, but trust me, it's totally manageable. We're going to take it slow and explain every detail. So, grab your calculators (or just your brainpower!) and let's dive in!

Understanding the Order of Operations

Before we even think about crunching numbers, it's super important to remember the order of operations. You might have heard of it as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Either way, it's the golden rule for solving math problems. This order ensures we all get to the same correct answer. Imagine the chaos if everyone did calculations in a different order!

Why is this order so crucial? Think of it like building a house. You need a solid foundation before you can put up the walls, right? Similarly, in math, certain operations need to be done before others to maintain the integrity of the equation and reach the correct solution. For example, exponents dictate how many times a number is multiplied by itself, reflecting a core scaling operation that needs to be calculated before addition or subtraction can properly reflect a number's change. Without a defined order, the entire mathematical structure would collapse, leading to ambiguity and incorrect results. We wouldn't want that, would we?

Following the correct order of operations ensures the consistent and logical resolution of mathematical expressions. It avoids ambiguity and guarantees that everyone arrives at the same, correct answer. In simpler terms, sticking to PEMDAS (or BODMAS) is our roadmap to mathematical success!

Step-by-Step Solution

Okay, let's apply our knowledge of the order of operations to the problem at hand: $\left(\frac{6}{2}\right)^2+7 \times 2$ . Remember PEMDAS/BODMAS!

1. Parentheses/Brackets

First up, we tackle what's inside the parentheses: $\frac{6}{2}$ . This is simply 6 divided by 2, which equals 3. So, we can rewrite the expression as:

$(3)^2 + 7 \times 2$

2. Exponents/Orders

Next, we deal with the exponent. We have $(3)^2$ , which means 3 squared, or 3 multiplied by itself: $3 \times 3 = 9$ . Now our expression looks like this:

$9 + 7 \times 2$

3. Multiplication and Division

Moving on, we perform the multiplication. We have $7 \times 2$ , which equals 14. The expression is now:

$9 + 14$

4. Addition and Subtraction

Finally, we perform the addition: $9 + 14 = 23$ .

So, the final answer is 23!

Breaking it Down Further

Let's recap each step to make absolutely sure we're all on the same page. Sometimes seeing it explained in slightly different words can really help solidify understanding.

Simplify Inside Parentheses: We started with $\left(\frac{6}{2}\right)^2+7 \times 2$ . The first task was to simplify the fraction inside the parentheses. 6 divided by 2 is 3, so the expression became $(3)^2 + 7 \times 2$ .
Handle the Exponent: The next step was to address the exponent. $(3)^2$ means 3 raised to the power of 2, which is $3 \times 3 = 9$ . The expression then transformed into $9 + 7 \times 2$ .
Multiplication Comes Next: Following the order of operations, we performed the multiplication. $7 \times 2$ equals 14, leading to the expression $9 + 14$ .
Final Addition: Finally, we added the two remaining numbers: $9 + 14 = 23$ . This gave us the final result.

Each of these steps are not interchangable; following them in the precise order described is paramount to ensuring you arrive at the correct answer. Jumping around in the order will invariably result in the wrong final solution.

Common Mistakes to Avoid

It's easy to make small mistakes when working through math problems. Here are a couple of common pitfalls to watch out for:

Forgetting the Order of Operations: This is the biggest one! Make sure you always follow PEMDAS/BODMAS. Doing operations in the wrong order will lead to an incorrect answer. Forgetting this rule is the mathematical equivalent of starting your construction projects without a blueprint.
Miscalculating Exponents: Double-check your exponent calculations. Remember that $3^2$ means $3 \times 3$ , not $3 \times 2$ . It's a simple mistake, but it can throw off your entire answer. An incorrect understanding of what exponents represent can cause major calculation errors.
Simple Arithmetic Errors: Even if you understand the concepts, it's easy to make a small addition or multiplication error. Take your time and double-check your work, especially under pressure. No matter how skilled someone is at mathematics, everyone is capable of making small arithmetic errors; be vigilant!

By being aware of these common mistakes, you can significantly improve your accuracy and confidence in solving mathematical problems. It's all about paying attention to detail and practicing consistently.

Practice Makes Perfect

The best way to get comfortable with these types of problems is to practice! Here are a few similar examples you can try on your own:

$(4/2)^2 + 5 \times 3$
$(8/4)^2 + 2 \times 6$
$(10/5)^2 + 3 \times 4$

Work through each of these problems, paying close attention to the order of operations. Check your answers with a calculator or ask a friend to check your work. The more you practice, the more confident you'll become!

Real-World Applications

You might be wondering, "When am I ever going to use this in real life?" Well, understanding the order of operations and basic math skills is actually incredibly useful in many everyday situations. Here are just a few examples:

Cooking: When following a recipe, you need to understand the order in which to add ingredients and adjust cooking times. This requires basic math skills and an understanding of sequence, similar to the order of operations.
Finance: Calculating interest, budgeting, and managing your finances all require math skills. Understanding how to calculate percentages, discounts, and interest rates is essential for making informed financial decisions. Getting something as simple as the order of operations mixed up when calculating the interest in your bank account can lead to some serious issues.
Home Improvement: Measuring materials, calculating areas, and estimating costs for home improvement projects all require math skills. Whether you're painting a room, building a deck, or installing new flooring, math is your friend.
Shopping: Comparing prices, calculating discounts, and determining the best deals all require math skills. Being able to quickly calculate percentages and compare unit prices can save you money.

So, even if you don't realize it, you're using math every day! The more comfortable you are with these basic concepts, the better equipped you'll be to handle real-world situations.

Conclusion

So there you have it! Solving $\left(\frac{6}{2}\right)^2+7 \times 2$ is all about remembering the order of operations and taking it one step at a time. Don't be afraid to break down the problem into smaller, more manageable parts. And remember, practice makes perfect! The more you work with these types of problems, the easier they'll become.

Keep practicing, stay curious, and you'll be a math whiz in no time! You got this!