Hey guys! Let's dive into a math problem that's as fresh as a bouquet from Simone's flower shop. We're going to break down a word problem step by step, making sure everyone understands how to solve it. Math can be fun, especially when it involves real-life scenarios, so let's get started!
The Question: Total Work Hours
Our main task is to figure out the total number of hours Simone's employees work each day. The question tells us that Simone has 5 employees, and each employee works $64 / 15$ hours per day. We need to find the combined hours of all employees. To do this, we'll perform a simple multiplication. This question is a classic example of how fractions can appear in everyday situations, and mastering it will help you tackle similar problems with confidence. Let's break down the math to make sure it's super clear. This might seem tricky at first, but don't worry; we'll go through it together. Remember, understanding each step is key to solving not just this problem, but many others like it. So, let's put on our thinking caps and get to work!
Breaking Down the Problem
First off, let’s underline the important information. We know:
- Simone has 5 employees.
- Each employee works $64 / 15$ hours a day.
To find the total hours, we multiply the number of employees by the hours each employee works. This is a fundamental concept in math – combining equal groups. In this case, we’re combining the work hours of each employee to find the total. Think of it like this: if one person works 2 hours, and you have 3 people, you'd multiply 2 by 3 to get the total hours worked. We're doing the same thing here, just with a fraction involved. So, the equation we need to solve is:
This looks a bit like a mouthful, but don't sweat it! We can simplify this before we even start multiplying. Simplifying fractions makes the multiplication process much easier and reduces the chances of making mistakes. Plus, it's a neat trick to have up your sleeve for future math problems. Okay, let’s simplify and get to the solution!
Solving the Equation
Now, let’s calculate the total hours. To multiply a whole number by a fraction, we can write the whole number as a fraction with a denominator of 1. So, 5 becomes $5 / 1$. Our equation now looks like this:
Before we multiply, let’s see if we can simplify. Notice that 5 and 15 have a common factor, which is 5. We can divide both 5 and 15 by 5:
- 5 divided by 5 is 1.
- 15 divided by 5 is 3.
Our equation simplifies to:
Now, we multiply the numerators (the top numbers) and the denominators (the bottom numbers):
So, the total hours worked by all employees is $64 / 3$ hours. But wait, the answer choices are in mixed numbers or whole numbers. We need to convert this improper fraction (where the numerator is greater than the denominator) into a mixed number.
Converting to a Mixed Number
To convert the improper fraction $64 / 3$ into a mixed number, we divide 64 by 3.
- How many times does 3 go into 64? It goes 21 times (21 x 3 = 63).
- We have a remainder of 1 (64 - 63 = 1).
So, the mixed number is 21 and 1/3. This means the employees work a total of $21 \frac{1}{3}$ hours per day. Now, let’s take a look at the answer choices and see if we've found the right one. And remember, if you ever get stuck on a fraction problem, just break it down step by step, and you'll get there!
Analyzing the Answer Choices
Alright, guys, let’s check out the answer choices provided. We calculated that the total hours worked by the employees are $21 \frac{1}{3}$ hours. Now, we need to match our answer with the options given. This step is crucial because it helps us confirm that we've done our math correctly and haven't made any silly mistakes along the way. It's like the final piece of the puzzle, ensuring everything fits perfectly.
Looking at the options:
A. $31 \frac{1}{3}$ B. 30 C. $30 \frac{2}{3}$
D. $21 \frac{1}{3}$
We can clearly see that option D, $21 \frac{1}{3}$, matches our calculated answer. This is fantastic news! It means we’ve correctly solved the problem and understood each step along the way. But before we celebrate too much, let’s quickly glance at the other options to make sure they’re definitely incorrect. This is a good habit to get into, as it reinforces your understanding and helps you avoid common errors. So, let’s give the other options a quick look and confirm our choice.
Why Other Options Are Incorrect
To be absolutely sure, let’s quickly analyze why the other options are incorrect. This helps reinforce our understanding and prevents us from second-guessing ourselves. Plus, it’s a great way to learn from potential mistakes and understand the problem even better.
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Option A: $31 \frac{1}{3}$
This is significantly higher than our calculated answer. If we mistakenly added the hours instead of multiplying, we might have gotten a number in this ballpark. So, this option is definitely incorrect.
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Option B: 30
This number is close, but still not the same as our answer. It might result from a miscalculation or rounding error. However, we know our exact answer is $21 \frac{1}{3}$, so 30 is not correct.
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Option C: $30 \frac{2}{3}$
Similar to option B, this is close but not quite right. It suggests a possible error in the final calculation or conversion to a mixed number. Again, our accurate result is $21 \frac{1}{3}$, making this option incorrect.
By ruling out these options, we can be even more confident in our choice of option D. It's always a good practice to double-check your work and understand why other options don't fit. This not only ensures you get the correct answer but also deepens your understanding of the underlying concepts.
Final Answer
Drumroll, please! After carefully working through the problem and analyzing the answer choices, we’ve confidently arrived at the solution. The total hours that the 5 employees work per day is $21 \frac{1}{3}$ hours. This corresponds to answer choice D.
So, the correct answer is:
D. $21 \frac{1}{3}$
We nailed it, guys! This problem demonstrates how important it is to break down complex questions into smaller, manageable steps. By understanding each step and double-checking our work, we can tackle even the trickiest math problems with confidence. Remember, practice makes perfect, so keep working on these types of problems, and you'll become a math whiz in no time!
Key Takeaways
Before we wrap up, let's highlight some key takeaways from this problem. These points will not only help you with similar questions but also improve your overall problem-solving skills in math.
- Read Carefully: Always read the question thoroughly and underline the important information. This helps you understand what’s being asked and prevents careless mistakes.
- Identify the Operation: Determine the correct mathematical operation needed to solve the problem. In this case, we needed to multiply the number of employees by the hours each employee works.
- Simplify When Possible: Look for opportunities to simplify fractions or expressions before performing calculations. This makes the math easier and reduces the chances of errors.
- Convert to the Correct Form: Ensure your answer is in the correct form, whether it’s a mixed number, decimal, or whole number. In this case, we converted an improper fraction to a mixed number.
- Check Your Work: Always double-check your calculations and compare your answer with the options provided. Eliminate incorrect choices to build confidence in your final answer.
By following these tips, you'll be well-equipped to handle similar problems and boost your math skills. Remember, math is all about practice and understanding the fundamentals. So, keep learning, keep practicing, and you'll conquer any math challenge that comes your way!
Practice Makes Perfect
To really solidify your understanding, try solving similar problems. You can even create your own scenarios, like figuring out the total hours worked in a bakery or a grocery store. The more you practice, the more comfortable you'll become with these types of calculations. And who knows, maybe one day you'll be running your own flower shop, just like Simone, and using these math skills in real life! Keep up the great work, guys, and happy calculating!