Math Problem: Finding A Number After Subtraction

by ADMIN 49 views

Hey guys! Let's dive into a fun math problem today. We're going to break down how to find a number when we know some information about it. This type of problem is super common in math, and once you get the hang of it, you'll be solving them like a pro. So, let's get started!

Understanding the Problem

Okay, so here's the question we're tackling: What is the result when 2 is subtracted from a number that is 14 when added to 5? Sounds a bit tricky, right? Don't worry, we'll take it step by step. The first thing we need to do is figure out exactly what the question is asking. It's like being a detective and gathering clues!

  • Key Information: The problem essentially gives us two main clues. The first clue is that there's a mystery number. Let's call this mystery number "x" for now. The question tells us that if we add 5 to this number (x), we get 14. Think of it like this: x + 5 = 14. The second clue is that we need to subtract 2 from this mystery number (x) after we've found out what x is. So, our final goal is to find out what x - 2 equals.
  • Breaking it Down: To make it even clearer, we can break the problem down into two smaller questions: What is the mystery number (x)? What do we get when we subtract 2 from that mystery number?

It’s like we're unwrapping a puzzle, piece by piece. By identifying these smaller parts, we're making the whole problem much less intimidating. We're not trying to jump to the answer right away; we're taking our time to understand what we need to do first. This is a crucial skill in math (and in life!), because often, complex problems become manageable when we break them into smaller steps. We'll use this strategy throughout our solution.

Finding the Original Number

Alright, so our first mini-mission is to find the original number. Remember, we know that if we add 5 to this number, we get 14. This is where we get to play with equations a little bit. Equations are just mathematical sentences that tell us two things are equal.

  • Setting up the Equation: We can write this information as an equation: x + 5 = 14. See how we just translated the words into math symbols? This is a super important skill in algebra. The "x" is still our mystery number, and the "=" sign means "is equal to".
  • Solving for x: Now, how do we figure out what "x" actually is? We need to isolate "x" on one side of the equation. Think of it like balancing a scale. Whatever we do to one side, we have to do to the other side to keep it balanced. Since we have "x + 5", we need to get rid of that "+ 5". The opposite of adding 5 is subtracting 5, so that's what we'll do! We subtract 5 from both sides of the equation: x + 5 - 5 = 14 - 5. Notice how we're keeping the equation balanced by doing the same thing on both sides.
  • Simplifying: Now, let's simplify. On the left side, +5 and -5 cancel each other out, leaving us with just "x". On the right side, 14 - 5 is 9. So, our equation becomes: x = 9. Ta-da! We found our mystery number! x is 9. This means the original number we were looking for is 9. We’ve solved the first part of our puzzle.

This step is like finding a key that unlocks the rest of the solution. Without knowing the original number, we can't move forward. So, make sure you're comfortable with the idea of setting up and solving simple equations like this. They're the building blocks for lots of other math problems!

Subtracting 2 from the Original Number

Okay, awesome! We've discovered that our original number is 9. Now for the final step: we need to subtract 2 from this number. This part is actually pretty straightforward compared to finding the original number, but it's just as crucial.

  • Setting up the Subtraction: The problem asks us to find what we get when we subtract 2 from our original number (which we now know is 9). So, we simply write this as: 9 - 2. This is a basic subtraction problem, and we're just translating the words into a mathematical operation.
  • Performing the Subtraction: Now, we just need to do the math. 9 - 2 equals 7. Easy peasy, right? This is why it’s so important to have a solid grasp of basic arithmetic. When we’re dealing with more complex problems, we don’t want to get bogged down by simple calculations.
  • The Final Answer: So, the answer to our question, "What is the result when 2 is subtracted from a number that is 14 when added to 5?" is 7. We did it! We took a word problem that seemed a little confusing at first and broke it down into manageable steps. We found the original number and then subtracted 2 from it. This is a really important skill in math, and it’s something you’ll use again and again.

It’s like we’ve built a little mathematical machine. We fed it the problem, it processed the information step-by-step, and it gave us the answer. The beauty of math is that it provides us with these tools and techniques to solve problems systematically.

Checking Our Work

Before we celebrate too much, let's do something super important: let's check our work! It's always a good idea to make sure our answer makes sense in the context of the original problem. Think of it as being a detective who double-checks all the evidence.

  • Reviewing the Steps: Let's quickly recap what we did. First, we figured out that the original number plus 5 equals 14. We solved for that number and found it to be 9. Then, we subtracted 2 from 9 and got 7. So, our answer is 7.
  • Plugging it Back In: Now, let's plug our answer back into the original problem to see if it works. The problem said that the original number plus 5 equals 14. Is 9 + 5 = 14? Yes, it is! Then, it asked what we get when we subtract 2 from that original number. Is 9 - 2 = 7? Yep! Our answer checks out. This is a fantastic way to build confidence in your solutions.
  • Why Checking is Important: Checking your work isn't just about getting the right answer. It's about building good habits. It helps you catch mistakes, understand the problem better, and solidify your knowledge. Plus, it's super satisfying when you know you've not only solved the problem but also verified your solution. It’s like putting the final piece in a jigsaw puzzle – you can see the whole picture clearly.

Tips for Solving Similar Problems

So, you've nailed this problem! But what about similar problems? No worries, guys! Here are a few tips and tricks to keep in your math toolkit for when you encounter problems like this in the future.

  • Read Carefully: This might sound obvious, but it's so important! Read the problem at least twice. The first time, just get a general idea of what it's about. The second time, focus on the specific details and information given. Underline or highlight key phrases and numbers. This active reading helps your brain process the information more effectively.
  • Break it Down: We've talked about this before, but it's worth repeating. Complex problems often feel overwhelming because we try to solve them all at once. Instead, break the problem down into smaller, more manageable parts. What is the problem really asking? What are the steps you need to take to get to the answer? It’s like climbing a mountain – you don’t try to jump to the top in one go; you take it one step at a time.
  • Identify Key Information: What are the essential pieces of information you need to solve the problem? Sometimes, problems will include extra information that you don't actually need. Learning to identify the key information helps you focus your efforts and avoid getting distracted. It’s like being a detective who knows what clues to follow and what leads to ignore.
  • Translate Words into Math: A huge part of solving word problems is being able to translate the words into mathematical symbols and equations. Practice identifying key words that indicate specific operations. For example, "sum" means addition, "difference" means subtraction, "product" means multiplication, and "quotient" means division. It's like learning a new language – you need to learn the vocabulary to understand the grammar.
  • Set up Equations: Once you've identified the key information and translated the words, try to set up an equation (or equations) that represents the problem. This helps you organize your thinking and gives you a clear roadmap for solving. Equations are like the blueprints for your solution.
  • Solve Step-by-Step: Once you have your equation, solve it step-by-step, showing your work. This helps you avoid mistakes and makes it easier to check your answer later. It also makes your thinking visible, which can be helpful if you get stuck and need to ask for help. It’s like writing out the recipe for a cake – each step is important.
  • Check Your Answer: Always, always check your answer! Plug your answer back into the original problem to see if it makes sense. Does it fit the context of the problem? Are the units correct? This simple step can save you from making careless mistakes. It’s the final quality control check.
  • Practice, Practice, Practice: The more you practice solving problems like this, the better you'll become. Don't be afraid to make mistakes – they're a natural part of the learning process. The important thing is to learn from your mistakes and keep trying. It’s like learning to ride a bike – you might fall a few times, but you’ll eventually get the hang of it.

Conclusion

So, guys, we've not only solved a math problem today but also learned some really valuable strategies for tackling similar problems in the future. Remember, math isn't just about getting the right answer; it's about the process of thinking, problem-solving, and building confidence in your abilities. You’ve seen how breaking down complex problems into smaller steps, setting up equations, and checking your work can make even tricky questions manageable. Keep practicing, stay curious, and you'll be amazed at what you can achieve! And remember, if you ever get stuck, don’t hesitate to ask for help – we’re all in this together!