Patio Cleanup: Fractions And Area Calculation

Hey everyone! Let's dive into a fun math problem that involves fractions, areas, and a bit of decorating. We've got a scenario where a group of people are cleaning up a patio, and we need to figure out what fraction of the patio was decorated and how many square meters that actually covers. So, grab your thinking caps, and let's get started!

Breaking Down the Cleaning Crew's Efforts

So, here's the deal: we have a group tackling a patio cleanup. The first group is super efficient and sweeps away 3/8 of the entire patio. That's a pretty good chunk! Then, we have a second group that's in charge of cleaning, and they manage to tidy up 1/4 of the patio. Awesome teamwork, guys!

But wait, there's more! After the sweeping and cleaning are done, there's still some decorating to do. We need to figure out what fraction of the patio is left for the decorators to work their magic on. This is where our fraction skills come into play.

To figure this out, we need to find the total fraction of the patio that was swept and cleaned. We'll do this by adding the fractions representing the work of the first two groups: 3/8 + 1/4. Now, we can't just add these fractions directly because they have different denominators (the bottom numbers). We need to find a common denominator, which is a number that both 8 and 4 divide into evenly. The smallest common denominator here is 8. So, we need to convert 1/4 into an equivalent fraction with a denominator of 8. To do this, we multiply both the numerator (top number) and the denominator by 2: (1 * 2) / (4 * 2) = 2/8.

Now we can add the fractions: 3/8 + 2/8. When we add fractions with the same denominator, we simply add the numerators and keep the denominator the same: (3 + 2) / 8 = 5/8. So, the first two groups together cleaned 5/8 of the patio. But what fraction is left for decorating? Well, the entire patio represents 1 whole, which we can also write as 8/8. To find the fraction that was decorated, we subtract the fraction cleaned from the whole: 8/8 - 5/8 = (8 - 5) / 8 = 3/8. Ta-da! The decorators get to work on 3/8 of the patio. It's like a fraction-tastic puzzle, isn't it?

From Fractions to Square Meters: Decorating the Space

Okay, so we know that the decorators are in charge of 3/8 of the patio. That's a great start! But now, let's add a little more real-world context to this problem. We're told that the entire patio measures 320 square meters. That's a pretty sizable space! Now, we want to figure out exactly how many square meters the decorating team will be working with. This is where we connect our fraction knowledge to a real measurement.

To find the area the decorators will be working on, we need to calculate 3/8 of the total patio area, which is 320 square meters. In math terms,