Solving Math Problems: A + C - B In Factor Trees

Hey guys! Let's dive into a fun math problem today. We're going to explore factor trees and solve an equation. Don't worry; it's not as scary as it sounds! We'll break it down step by step, making sure everyone understands how to crack this problem. We will explain the provided factor tree and show you how to find the values of A, B, and C, and then, we'll find the final answer. This is a great way to improve your math skills and understand how factor trees work. By understanding the concept, you'll be able to solve similar problems with ease. So, grab a pen and paper, and let's get started. Let's get started and make sure you follow along, and I'll make sure you understand everything. Are you ready to get started? Let's do it.

Understanding the Factor Tree

Alright, first things first: what's a factor tree? It's a cool visual way to break down a number into its prime factors. Think of it like a family tree, but instead of people, you have numbers. Each branch splits into factors until you reach the prime numbers (numbers that can only be divided by 1 and themselves). In our problem, we have a partial factor tree with some numbers missing, represented by A, B, and C. Our goal is to figure out those missing numbers and then use them to solve the equation A + C - B. It is all about seeing what goes where. Let's say that we are given a number, then that number must be broken down until we get to the prime numbers. So the tree will show you how those numbers were broken down. Do you guys get it? If you follow the tree, you can see how everything is broken down. If you understand this, you can understand this problem.

In the factor tree, we know that the number 4 branches out into 3 and A. The number A then branches into 2 and B. The number C branches out into 5 and 7. Do you see how we can work with this? The important thing to remember here is that each branch tells us the factors that we must multiply to get the value above them. Do you guys know how to do this? This method is used to help in solving the problem. So, to solve this problem, we have to solve for each letter and then perform the operations that are required in the problem. So, we can start to see how the value of the factors work. Do you see how this is working? Pretty simple, right?

Identifying the Numbers

Now, let's start by figuring out the missing values. If you look at the factor tree, we know that the initial number branches out to 4, 3, A, 2, B, C, 5, and 7. Let's see what we can infer from this information. When you follow the branch and multiply them together, you get the original number. So to find A, we need to multiply 3 by A. Therefore, A must be 4 * 3, which equals 12. Next, we can see that A branches out to 2 and B. Therefore, we know that the result of the multiplication of 2 and B equals 12. Since we know that 2 * B equals 12, we can infer that B must be 6. Finally, we can see that C must be the result of multiplying 5 and 7, which equals 35. Now that we've found the values of A, B, and C, we can move on to the next step.

Calculating the Values

Now that we understand the structure of a factor tree, let's break down how to find the values of A, B, and C. This is the part where we do some number crunching and figure out the missing pieces of the puzzle. We'll use the information provided by the factor tree to identify the relationships between the numbers and determine the correct values. This part is not hard; you just need to follow each step carefully, and I'll be right here to guide you. We're trying to find the missing values. So, we have to understand what we are given and what we are trying to find. Are you ready to find out the missing values?

Finding the Value of A

Let's focus on finding the value of A. Looking at the top of the tree, we see that the branch splits into 4, 3, and A. So, we know that the product of 4 must be equal to 12. Now, to find A, we'll just follow the branches. We know that 4 must branch out into 2 and B. So we know that A is the product of 2 and B. So, we know that the numbers must be 12. Do you follow? Therefore, the number is 12. Simple, right?

Finding the Value of B

Next up, let's figure out B. We now know that A is 12 and that A splits into 2 and B. So, we can infer that A, which is 12, is the result of multiplying 2 and B. So, if you know that A is 12, and one part of the product is 2, the other part must be 6. Therefore, B must be 6. Good job, everyone! You're doing great.

Finding the Value of C

Finally, let's find C. If you look at the factor tree, you can see that C branches into 5 and 7. This is pretty straightforward. The value of C is simply the product of 5 and 7. Easy, right? So, C = 5 * 7 = 35. Nice work, guys! Now that we have all the values, we can move on to the final step: solving the equation!

Solving the Equation A + C - B

Alright, now that we've found the values of A, B, and C, we're ready to solve the equation A + C - B. This is the final step, where we put everything together and get our answer. It's like assembling the pieces of a puzzle. Once we substitute the values we found into the equation, we can perform the calculations and arrive at the correct result. This step will be easy for you guys because we did the hard work already. Are you ready to finish this up? Then, let's get started.

Substituting the Values

So, remember that A = 12, B = 6, and C = 35. Now, let's substitute these values into the equation A + C - B. It will look like this: 12 + 35 - 6. See? We just replaced the letters with their numerical values. Nothing to worry about, right? Now it's time to do some simple math.

Performing the Calculations

Now that we've plugged in the values, let's do the math! We have 12 + 35 - 6. First, we add 12 and 35, which equals 47. Then, we subtract 6 from 47. The result is 41. So, A + C - B = 41. Great job, everyone! We solved the problem together. It was fun, right? We used the factor tree to find the values, and then we used those values to solve the given equation. You guys are awesome!

Final Answer and Conclusion

So, guys, we did it! We started with a factor tree, found the values of A, B, and C, and finally solved the equation A + C - B. The final answer is 41. This whole process showed you how factor trees work, how to break down numbers, and how to use those numbers to solve equations. It also helps to improve your critical thinking and analytical skills. Do you know you can use this method to solve other problems? So go ahead and practice! The more you practice, the better you'll get. Keep up the great work, and I'll see you in the next math adventure!