Math Problems: Compose Expressions & Find Solutions

Hey guys! Let's dive into some fun math problems where we'll learn to create expressions and find the answers. We've got two problems here that involve a little bit of thinking and a dash of arithmetic. So, grab your pencils and let's get started!

Problem A: The Tracks

Let's break down this track problem step by step. Keywords here are length, shorter, and both tracks. We know one track is 36 meters long. The other track's length is described in relation to the first one – it's 6 times shorter. This means we need to divide the length of the first track by 6 to find the length of the second track. So, how do we put this into an expression? First, we calculate the length of the shorter track: 36 meters / 6 = 6 meters. Now, we need to find the total length of both tracks. To do that, we simply add the length of the first track to the length of the second track. That's 36 meters + 6 meters = 42 meters. So, our final answer is 42 meters. Remember, when you're tackling math problems like this, always highlight the keywords and think about what operations (addition, subtraction, multiplication, division) they suggest. Breaking the problem down into smaller steps makes it much easier to solve. And always double-check your work to make sure you haven't made any silly mistakes!

The key to solving this kind of problem is understanding the relationship between the different pieces of information. In this case, the phrase "6 times shorter" is crucial. It tells us we need to perform a division operation. If it said "6 times longer," we would need to multiply instead. Also, don't forget the final step! The question asks for the total length of both tracks, so we need to add the lengths together. It's easy to calculate the length of the shorter track and then forget to add it to the length of the longer track. Pay close attention to what the question is asking, and make sure your answer addresses that specific question. This is a common mistake, even for people who are good at math, so train yourself to always read the question carefully before you start calculating. Keep practicing problems like this, and you'll become a pro at setting up expressions and finding solutions!

Problem B: The Bus Ride

Now, let's hop on the bus and solve this one! This problem involves figuring out how many people were on the bus in total, and it throws in a little twist. We know there were 8 children on the bus, and that number is 5 times less than the number of adults. Our keywords are children, less, adults, and total. This means there were more adults than children. To find the number of adults, we need to do the opposite of what "5 times less" might initially suggest. Instead of dividing, we'll multiply the number of children by 5. So, the calculation is 8 children * 5 = 40 adults. Great! We've figured out how many adults were on the bus. But we're not done yet! The problem asks for the total number of people on the bus, so we need to add the number of children and the number of adults together. That's 8 children + 40 adults = 48 people. So, in total, there were 48 people on the bus. Just like the first problem, it's crucial to read the question carefully. The phrase "5 times less" can be a bit tricky. It doesn't mean we divide; it means the number of adults is 5 times greater than the number of children. Always think about the relationships between the numbers and what the words imply. And again, make sure you answer the question that's being asked! It's easy to find the number of adults and stop there, but the problem specifically asks for the total number of people.

To master these types of problems, practice identifying those key phrases that indicate which operation to use. Phrases like "times less" often mean you need to multiply, while phrases like "times more" mean the opposite. The more you practice, the quicker you'll become at recognizing these patterns and setting up the correct expressions. And don't be afraid to draw a diagram or visualize the problem. Sometimes, seeing the problem laid out in a visual way can help you understand the relationships between the numbers better. So, keep practicing, keep thinking, and you'll become a math whiz in no time!

Key Takeaways

Alright, guys, we've tackled two interesting math problems today! Let's recap the key strategies we used to solve them. First and foremost, always read the problem carefully and identify the keywords. These words are like clues that point you in the right direction. In the track problem, words like "shorter" and "both tracks" helped us understand what operations to perform. In the bus problem, words like "less" and "total" were our guiding lights.

Next, break the problem down into smaller, more manageable steps. Don't try to solve everything at once. Figure out what information you have and what you need to find. For example, in the track problem, we first calculated the length of the shorter track, and then we added it to the length of the longer track. In the bus problem, we first found the number of adults, and then we added it to the number of children. Breaking the problem down makes it less overwhelming and reduces the chances of making mistakes.

Another crucial step is to think about the relationships between the numbers. What does it mean when something is "5 times less" than something else? What does it mean when you need to find the "total"? Understanding these relationships is essential for choosing the correct operations. If you're not sure, try drawing a picture or using a real-world example to help you visualize the problem.

And finally, always double-check your work! It's easy to make a silly mistake, especially when you're dealing with multiple steps. Take a few extra seconds to review your calculations and make sure your answer makes sense in the context of the problem. Did you answer the question that was actually asked? Is your answer a reasonable number? These simple checks can save you a lot of points!

So, guys, remember these strategies, and you'll be well on your way to becoming math problem-solving masters! Keep practicing, keep thinking, and most importantly, have fun with it!