Solve: Operator For (10 ? 6) × 3 = 12
Hey there, math enthusiasts! Today, we're diving into a fun little equation puzzle. We need to figure out which mathematical operator—you know, like addition, subtraction, multiplication, or division—will make the statement (10 ? 6) × 3 = 12 true. Sounds like a brain-tickling challenge, right? So, grab your thinking caps, and let's get started!
Understanding the Problem
Before we jump into solving, let's make sure we understand what the question is asking. We have an equation with a missing operator: (10 ? 6) × 3 = 12. Our mission, should we choose to accept it (and we do!), is to replace the question mark with the correct mathematical operator (+, -, ×, or ÷) so that the equation holds true. In other words, after performing the operation inside the parentheses and then multiplying the result by 3, we should end up with 12. This is a classic problem-solving scenario where we'll use a bit of trial and error combined with our knowledge of basic arithmetic. Remember, math isn't just about memorizing formulas; it's about understanding relationships and using logic to find solutions. So, let's break down the problem step by step and explore different possibilities.
Breaking Down the Equation
To effectively solve this, we need to think about the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our case, we have parentheses, so the operation inside them needs to be performed first. Then, we multiply the result by 3. The ultimate goal is to get 12 on the right side of the equation. This means we need to figure out what number, when multiplied by 3, equals 12. That's our first clue! By working backward and thinking strategically, we can narrow down the possibilities and find the operator that fits perfectly. So, let's start with that crucial first step: what number times 3 equals 12? Knowing this will give us a target for the result inside the parentheses, making the rest of the puzzle much easier to solve. Are you ready to put on your detective hat and uncover the missing operator? Let's do it!
Testing the Operators: A Step-by-Step Approach
Okay, guys, let's get down to business and test out those operators one by one. Remember, we're looking for the operator that, when placed in the equation (10 ? 6) × 3 = 12, will make the equation true. We'll go through each of the basic operators—addition, subtraction, multiplication, and division—and see which one fits the bill. It's like a mathematical mystery, and we're the detectives!
1. Trying Addition (+)
Let's start with the plus sign. If we replace the question mark with addition, our equation becomes (10 + 6) × 3 = 12. First, we need to solve the operation inside the parentheses: 10 + 6 equals 16. Now, we have 16 × 3. What's that equal to? It's 48. So, the equation becomes 48 = 12. Hmm, that's not right! 48 is definitely not equal to 12. So, addition doesn't seem to be the correct operator in this case. But hey, that's okay! We've only just begun our investigation. One operator down, three to go. Let's keep going and see what the next operator brings.
2. Trying Subtraction (-)
Alright, let's move on to subtraction. This time, our equation looks like this: (10 - 6) × 3 = 12. Again, we start with the parentheses. 10 minus 6 equals 4. So now we have 4 × 3. What's 4 times 3? It's 12! Bingo! The equation now reads 12 = 12. That's a match! It seems like subtraction is the operator we were looking for. But just to be absolutely sure, and for the sake of thoroughness, let's quickly check the remaining operators. It's always good to double-check your work, especially in math. So, let's see if multiplication or division could also possibly work.
3. Trying Multiplication (×)
Okay, let's try multiplication. If we use multiplication, the equation becomes (10 × 6) × 3 = 12. First, we solve inside the parentheses: 10 times 6 is 60. So now we have 60 × 3. What's 60 multiplied by 3? It's 180. That gives us the equation 180 = 12. Definitely not true! 180 is way bigger than 12. So, multiplication is not the correct operator for this equation. We're getting closer to confirming our answer, but let's check that last operator just to be 100% sure.
4. Trying Division (÷)
Last but not least, let's try division. With division, our equation is (10 ÷ 6) × 3 = 12. Okay, 10 divided by 6 is not a whole number; it's approximately 1.67. So, we have approximately 1.67 × 3. If we multiply that, we get about 5. This gives us the equation 5 = 12, which is also not true. So, division doesn't work either. We've now tested all four basic operators, and only one made the equation true. It looks like our detective work has paid off!
The Solution: Subtraction is the Key!
Drumroll, please! After carefully testing each operator, we've found the one that makes the statement (10 ? 6) × 3 = 12 true. The correct operator is subtraction (-). When we replace the question mark with a minus sign, the equation becomes (10 - 6) × 3 = 12. And as we calculated, 10 minus 6 is 4, and 4 times 3 is indeed 12. So, 12 = 12, and the equation holds perfectly. Woo-hoo! We cracked the code! This little puzzle demonstrates how important it is to understand the order of operations and how trying different possibilities can lead us to the right answer. Math is like a puzzle, and we've just fit the right piece into place.
Why Subtraction Works
But let's take a moment to think about why subtraction worked in this particular equation. The key lies in the target number we needed to achieve inside the parentheses. Since we were multiplying by 3 to get 12, we knew the result inside the parentheses had to be 4 (because 4 × 3 = 12). Subtraction was the only operation that could give us 4 when applied to 10 and 6. This kind of reverse thinking—working backward from the desired result—is a powerful problem-solving strategy in mathematics and in life. It helps us break down complex problems into smaller, more manageable steps. So, remember, when faced with a challenge, try to identify your goal and then think about the steps needed to get there. You might be surprised at how effective this approach can be!
Conclusion: Math is an Adventure!
So there you have it, guys! We successfully solved the equation (10 ? 6) × 3 = 12 by figuring out that the missing operator was subtraction. We did it by systematically testing each of the basic operators and seeing which one fit. This kind of problem-solving is what makes math so engaging and rewarding. It's not just about memorizing facts; it's about using logic and reasoning to unravel mysteries. Remember, every equation is a puzzle waiting to be solved, and every mathematical problem is an opportunity to learn and grow.
Keep Exploring the World of Math
I hope you had fun working through this problem with me. Math is a vast and fascinating world, full of challenges and discoveries. Keep exploring, keep questioning, and keep solving! Whether it's figuring out the tip at a restaurant, calculating the distance on a road trip, or tackling complex algebraic equations, the skills you develop in math will serve you well in all areas of life. So, embrace the challenge, enjoy the journey, and never stop learning. And who knows? Maybe next time, we'll explore even more complex and exciting mathematical puzzles together. Until then, keep those brains buzzing and those pencils moving!