Rustam's Height: A Math Problem Solved Simply

Hey guys! Today, we're diving into a fun math problem that involves figuring out someone's height based on a fraction of another person's height. It's like a little detective work with numbers, and I promise it's not as scary as it sounds! We'll break it down step by step so you can see exactly how it's done. So, let's jump right into this height-calculating adventure!

Understanding the Problem: Maryam and Rustam's Heights

Let's break down this word problem bit by bit, making sure we understand what we're trying to solve. The core of the problem revolves around understanding proportional relationships, a key concept in mathematics. We're told that Maryam's height is 98 cm. This is our starting point, our known value. Then comes the interesting part: Rustam's height isn't given as a direct number, but as a fraction of Maryam's height. Specifically, Rustam's height is 12/7 of Maryam's height. This fraction, 12/7, is crucial. It tells us that Rustam is taller than Maryam because 12/7 is greater than 1 (if the fraction was less than 1, Rustam would be shorter). So, what are we actually trying to find? The problem clearly asks us to find Rustam's height in centimeters. We need to use the information we have – Maryam's height and the fractional relationship between their heights – to calculate Rustam's exact height. Word problems like these aren't just about numbers; they're about real-world scenarios. Think about it: you might use similar calculations when scaling recipes, figuring out discounts, or even understanding proportions in art and design. That's why mastering these types of problems is super useful. Before we jump into the calculations, let's recap: Maryam is 98 cm tall, Rustam is 12/7 of Maryam's height, and our goal is to find Rustam's height. Now that we've got a solid grasp of what we're dealing with, we can move on to the next step: figuring out how to actually solve it! Remember, breaking down the problem like this makes it way less intimidating, and you're already halfway to the solution just by understanding the question.

Calculating Rustam's Height: Step-by-Step

Okay, guys, now for the fun part – the actual calculation! To find Rustam's height, we need to apply the concept of fractions and multiplication. We know Rustam's height is 12/7 of Maryam's height. In math, the word "of" often indicates multiplication. So, we're going to multiply the fraction 12/7 by Maryam's height, which we know is 98 cm. Here's the equation we'll use:

Rustam's height = (12/7) * 98 cm

Now, let's break down the multiplication. There are a couple of ways we can tackle this. One way is to first multiply 12 by 98, and then divide the result by 7. However, there's a slightly easier method that can save us some time and effort. We can simplify the calculation by first dividing 98 by 7. Why? Because 98 is divisible by 7! 98 divided by 7 is 14. This simplifies our equation to:

Rustam's height = 12 * 14 cm

See how much simpler that looks? Now we just need to multiply 12 by 14. If you know your multiplication tables, this might be a breeze! If not, you can always do it the long way or use a calculator. 12 multiplied by 14 is 168. So, we've arrived at our answer:

Rustam's height = 168 cm

That's it! We've successfully calculated Rustam's height. But before we move on, let's just take a moment to double-check our work. Does 168 cm seem like a reasonable answer? Remember, we knew Rustam was taller than Maryam (98 cm) because the fraction 12/7 is greater than 1. 168 cm is indeed greater than 98 cm, so our answer seems to make sense. This step of checking your answer is super important in math (and in life in general!). It helps you catch any silly mistakes and ensures you're confident in your solution. Now that we've got the answer and we've checked our work, let's move on to the final step: stating our solution clearly.

Stating the Solution Clearly: Rustam's Height is Revealed

Alright, we've done the hard work of understanding the problem and crunching the numbers. Now, let's make sure we present our solution in a clear and understandable way. This is a crucial step because simply arriving at the correct number isn't enough; you need to communicate your answer effectively. So, what's the best way to state our solution? We need to answer the question that was originally asked: "What is Rustam's height?" Based on our calculations, we know Rustam's height is 168 cm. Therefore, a clear and concise way to state the solution is:

Rustam's height is 168 cm.

See how straightforward that is? We've answered the question directly, using the correct units (centimeters). It's important to always include the units in your answer when dealing with measurements. Imagine if we just said "Rustam's height is 168." 168 what? Meters? Millimeters? The units give our answer context and meaning. In this case, centimeters tell us we're talking about a person's height in a standard measurement unit. Stating the solution clearly isn't just about getting the right answer; it's about showing your understanding of the problem. It tells the person reading your solution that you not only know the number, but you also know what it represents. So, remember, always state your solution clearly and completely, with the correct units, to make sure your hard work is fully appreciated. We've now successfully solved the problem of Rustam's height! But what have we really learned in the process? Let's recap the key concepts and takeaways from this math adventure.

Key Takeaways: Mastering Math Problems with Confidence

Okay, guys, we've reached the end of our math journey for today! We successfully calculated Rustam's height, but more importantly, we've reinforced some key mathematical concepts and problem-solving skills. Let's quickly recap what we've learned, so you can tackle similar problems with confidence in the future. First, we revisited the idea of proportional relationships. We saw how Rustam's height was related to Maryam's height through a fraction. Understanding these relationships is crucial in many areas of math and real life, from scaling recipes to understanding maps. Next, we practiced working with fractions, specifically multiplying a fraction by a whole number. This is a fundamental skill in arithmetic, and it's something you'll use again and again. Remember, the word "of" often means multiplication in math problems, so keep that in mind. We also saw the power of simplifying calculations. By dividing 98 by 7 before multiplying by 12, we made the problem much easier to manage. Looking for opportunities to simplify is a great strategy in math (and in life!). And let's not forget the importance of checking your work. We took a moment to make sure our answer (168 cm) made sense in the context of the problem. This simple step can save you from making careless errors. Finally, we emphasized the importance of stating your solution clearly and completely, with the correct units. Communication is key in math, just like it is in everything else. So, what's the biggest takeaway from this problem? It's that math problems, even word problems, aren't scary monsters. By breaking them down step by step, understanding the concepts involved, and practicing regularly, you can conquer any mathematical challenge that comes your way. So, keep practicing, keep asking questions, and keep exploring the wonderful world of math! You've got this!