Parking Lot Fractions Solving A Math Problem
Hey there, math enthusiasts! Let's dive into a cool problem that mixes math with a real-life scenario – parking lots! Ever wondered how fractions can help us understand the relationship between available parking spaces and the total number of spaces? Well, buckle up, because we're about to find out. This isn't just about numbers; it's about seeing how math applies to the world around us. So, let's get started and unravel this parking lot puzzle together!
The Parking Lot Problem: A Fraction Challenge
Okay, guys, here’s the deal. Imagine we have a parking lot – a big one – with a total of 300 parking spaces. Now, 180 of these spots are already taken by cars. The question we need to crack is this: What fraction represents the relationship between the number of available parking spaces and the total number of parking spaces in the lot? We have some options to choose from:
- A) 1/3
- B) 2/5
- C) 2/3
- D) 1/2
This problem is a fantastic way to see how fractions work in everyday situations. We're not just crunching numbers here; we're actually visualizing a real-world scenario. To solve this, we'll need to figure out how many spaces are free and then compare that number to the total number of spaces. It's like making a pizza and figuring out what fraction of the pizza is left after you've eaten a few slices. So, let's put on our thinking caps and get to work on this parking lot puzzle!
Breaking Down the Problem: Finding Available Spaces
Alright, the first step in solving this parking lot problem is to figure out how many parking spaces are actually available. We know the parking lot has a total of 300 spaces, and 180 of them are occupied. So, how do we find the number of free spaces? It’s simple subtraction, my friends! We need to subtract the number of occupied spaces from the total number of spaces. This will give us the number of spaces that are still up for grabs. Think of it like this: if you have a box of 300 cookies and you eat 180, how many cookies are left? The same logic applies here.
So, let’s do the math: 300 (total spaces) – 180 (occupied spaces) = ? What do we get? Exactly! We have 120 available parking spaces. Now that we know this crucial piece of information, we’re one step closer to solving the puzzle. But we're not done yet. We've only found the number of available spaces; now we need to express this as a fraction of the total number of spaces. This is where things get really interesting, so stick with me!
Expressing the Relationship as a Fraction: Available Spaces vs. Total Spaces
Okay, now that we know there are 120 available spaces, we need to express this as a fraction of the total number of spaces, which is 300. Remember, a fraction is just a way of showing a part of a whole. In this case, the 'part' is the number of available spaces, and the 'whole' is the total number of spaces. So, how do we write this as a fraction? Easy peasy! We put the number of available spaces (120) over the total number of spaces (300).
This gives us the fraction 120/300. But hold on a second! This fraction looks a bit clunky, doesn't it? It's like having a messy desk – it works, but it could be much cleaner and simpler. That's where simplifying fractions comes in. Simplifying a fraction means reducing it to its simplest form, where the numerator (the top number) and the denominator (the bottom number) have no common factors other than 1. Think of it like this: 120/300 is like a big, complicated puzzle, and simplifying it is like putting the puzzle pieces together to make a clearer picture. So, let's roll up our sleeves and simplify this fraction!
Simplifying the Fraction: Finding the Simplest Form
Alright, let’s get this fraction 120/300 into its simplest form. Simplifying fractions is like decluttering – we want to make it as neat and tidy as possible. To do this, we need to find the greatest common factor (GCF) of both the numerator (120) and the denominator (300). The GCF is the largest number that divides evenly into both numbers. It’s like finding the biggest measuring cup that you can use to measure both 120 cups of water and 300 cups of water exactly.
There are a couple of ways we can find the GCF. One way is to list out all the factors of each number and see which one is the biggest one they have in common. But that can take a bit of time. A quicker way is to start dividing both numbers by common factors until we can't anymore. For example, we can see that both 120 and 300 are divisible by 10. So, let’s divide both by 10. This gives us 12/30. Are we done yet? Nope! We can see that both 12 and 30 are divisible by 6. So, let’s divide both by 6. This gives us 2/5. Now, can we simplify it any further? Nope! 2 and 5 have no common factors other than 1, so we’ve reached the simplest form. So, 120/300 simplified is 2/5. This means that the fraction representing the relationship between available parking spaces and the total number of spaces is 2/5. Woohoo! We’ve cracked it!
Identifying the Correct Answer: Matching the Simplified Fraction
Okay, mathletes, we've done the hard work! We figured out that there are 120 available parking spaces, expressed the relationship as the fraction 120/300, and then simplified it to 2/5. Now comes the fun part: matching our answer to the options given in the problem. Remember those options?
- A) 1/3
- B) 2/5
- C) 2/3
- D) 1/2
We need to see which of these options matches our simplified fraction of 2/5. It’s like a matching game, but with fractions! We’ve got our answer, and now we just need to find its twin. So, let's take a look. Option A is 1/3, which is different from 2/5. Option B is… wait for it… 2/5! Bingo! We’ve found our match. Options C and D are 2/3 and 1/2, respectively, which are also different from our answer. So, the correct answer is B) 2/5. Pat yourselves on the back, guys! You've successfully navigated this parking lot problem and shown how fractions can help us understand real-world situations. You're not just solving math problems; you're becoming math detectives!
Real-World Application: Why This Matters
Now, you might be thinking,
