When it comes to solving math problems, following the correct order of operations is crucial. A common mistake people make is forgetting the standard rules that guide how we solve equations. Take, for instance, the equation:
At first glance, it might seem simple, but there’s a catch. If you solve this equation from left to right, as many people tend to do, you’ll get the wrong answer. So, what’s the right way to solve this, and why is the answer 46? Let’s break it down step by step, following the proper mathematical rules.
Understanding the Order of Operations
In mathematics, the order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure everyone gets the same correct result. The acronym PEMDAS is often used to remember this order:
- P: Parentheses first
- E: Exponents (i.e., powers and square roots, etc.)
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
Multiplication and division are performed before addition and subtraction unless parentheses are involved. So, how does this apply to our equation?
Breaking Down the Equation: 6 + 6 x 6 + 4
Let’s tackle the equation step by step using PEMDAS:
- Start with multiplication: According to the order of operations, multiplication comes before addition. So, the first step is to solve 6 x 6, which gives us 36.Now, the equation looks like this:
6 + 36 + 4
- Move to addition: After performing the multiplication, we move on to addition. Now we can solve the rest of the equation from left to right.First, add 6 + 36, which gives you 42.
42 + 4
- Complete the final addition: Finally, add the last part, 42 + 4, which equals 46.
The Correct Answer: 46
Following the order of operations, the correct answer to 6 + 6 x 6 + 4 is indeed 46. If you were to simply go from left to right without considering PEMDAS, you might mistakenly add 6 + 6 first, then multiply that result by 6, leading to a wrong answer.
Why People Get It Wrong
It’s easy to see why so many people get tripped up by this kind of problem. The natural instinct is to tackle the equation from left to right, ignoring the rule that multiplication should be done first. This is why remembering PEMDAS is so important—it ensures that we all arrive at the same, correct solution.
Many people make this mistake with more complex equations as well, which can lead to incorrect answers. However, once you’re familiar with the correct order of operations, solving these kinds of problems becomes much easier.
Practice Makes Perfect
The best way to get comfortable with the order of operations is through practice. When faced with a math problem like 6 + 6 x 6 + 4, always stop and think about PEMDAS before diving in. Doing so will help you avoid common pitfalls and ensure that you’re consistently getting the right answer.
Final Thoughts
In math, precision is everything. Understanding the order of operations is key to solving equations correctly, and it’s a skill that will serve you well in all sorts of mathematical problems. So, next time you see a problem like 6 + 6 x 6 + 4, you’ll know exactly how to solve it—and why the answer is 46!
