Calculating Fabric Leftover A Math Problem For Sharyn's Dresses

Hey everyone! Let's dive into a fun math problem about fabric, dresses, and leftovers. Sharyn is making dresses for herself and her daughter, and we need to figure out how much fabric she'll have left over after her project. This is a practical math problem that many people who sew or do crafts might encounter, so let's break it down step by step.

Understanding the Problem

In this fabric calculation scenario, Sharyn needs a specific amount of fabric for two dresses: one for herself and one for her daughter. The problem gives us the fabric requirements in mixed numbers, which might seem a bit tricky at first, but don't worry, we'll tackle it together. She needs $3 \frac{3}{8}$ yards for her dress and $2 \frac{1}{8}$ yards for her daughter's dress. Sharyn decides to buy $6 \frac{1}{8}$ yards of fabric. The question we need to answer is: how much fabric will Sharyn have left over after she makes both dresses? To solve this, we'll need to use addition to find the total fabric needed and subtraction to find the leftover amount. This problem is a great example of how fractions and mixed numbers are used in real-life situations, like sewing and crafting projects.

Step 1: Calculate the Total Fabric Needed

First things first, we need to figure out the total amount of fabric Sharyn needs for both dresses. She requires $3 \frac{3}{8}$ yards for her dress and $2 \frac{1}{8}$ yards for her daughter's dress. To find the total, we'll add these two amounts together. When adding mixed numbers, it's often easiest to add the whole numbers and the fractions separately. So, we add 3 and 2 to get the total whole yards needed, and then we add the fractions $\frac{3}{8}$ and $\frac{1}{8}$ to find the total fractional yards needed. Remember, when adding fractions, the denominators (the bottom numbers) must be the same. In this case, they already are, which makes it super convenient! Once we add the whole numbers and the fractions, we'll have the total fabric Sharyn needs. This step is crucial because it sets the foundation for the next step, where we'll subtract this total from the amount of fabric she bought. Getting this addition right is key to solving the problem accurately.

Step 2: Calculate the Fabric Left Over

Now that we know the total amount of fabric Sharyn needs, we can figure out how much she'll have left over. She bought $6 \frac{1}{8}$ yards of fabric, and we've calculated the total fabric needed for the dresses. To find the leftover amount, we'll subtract the total fabric needed from the amount she bought. This involves subtracting mixed numbers, which, like addition, can be simplified by subtracting the whole numbers and fractions separately. We'll subtract the total whole yards needed from the 6 whole yards Sharyn bought, and then we'll subtract the fractional yards needed from the $\frac{1}{8}$ yard she bought. If the fraction we're subtracting is larger than $\frac{1}{8}$, we'll need to borrow from the whole number, which is a common step in mixed number subtraction. The result of this subtraction will tell us exactly how much fabric Sharyn has left over. This is the final step in solving the problem and gives us the answer we're looking for.

Solving the Problem Step-by-Step

Okay, let's put on our math hats and work through this problem together, step by step. We'll break it down into manageable chunks to make it super clear and easy to follow. Remember, the key to solving word problems is to take them one step at a time and make sure you understand what you're doing at each stage. So, let's get started!

Step 1: Adding the Fabric Needed

First, we need to find the total fabric Sharyn needs. She needs $3 \frac{3}{8}$ yards for her dress and $2 \frac{1}{8}$ yards for her daughter's dress. Let's add these together:

$3 \frac{3}{8} + 2 \frac{1}{8}$

Add the whole numbers:

$3 + 2 = 5$

Add the fractions:

$\frac{3}{8} + \frac{1}{8} = \frac{4}{8}$

Combine the whole number and the fraction:

$5 + \frac{4}{8} = 5 \frac{4}{8}$

Simplify the fraction ($\frac{4}{8}$ can be simplified to $\frac{1}{2}$):

$5 \frac{4}{8} = 5 \frac{1}{2}$

So, Sharyn needs a total of $5 \frac{1}{2}$ yards of fabric. Remember, simplifying fractions is always a good practice as it makes the numbers easier to work with in the long run. In this case, reducing $\frac{4}{8}$ to $\frac{1}{2}$ makes our final answer cleaner and more understandable. This first step is crucial because it gives us the total fabric requirement, which we'll use in the next step to find out how much fabric Sharyn has left over.

Step 2: Subtracting to Find Leftover Fabric

Now that we know Sharyn needs $5 \frac{1}{2}$ yards of fabric, we can subtract this from the amount she bought, which is $6 \frac{1}{8}$ yards. This subtraction will tell us how much fabric she has left over:

$6 \frac{1}{8} - 5 \frac{1}{2}$

First, we need a common denominator to subtract the fractions. The least common denominator for 8 and 2 is 8. So, we'll convert $\frac{1}{2}$ to a fraction with a denominator of 8:

$\frac{1}{2} = \frac{1 imes 4}{2 imes 4} = \frac{4}{8}$

Now we can rewrite the subtraction:

$6 \frac{1}{8} - 5 \frac{4}{8}$

Since we can't subtract $\frac{4}{8}$ from $\frac{1}{8}$ directly, we need to borrow 1 from the whole number 6:

$6 \frac{1}{8} = 5 + 1 \frac{1}{8} = 5 + \frac{8}{8} + \frac{1}{8} = 5 \frac{9}{8}$

Now we can subtract:

$5 \frac{9}{8} - 5 \frac{4}{8}$

Subtract the whole numbers:

$5 - 5 = 0$

Subtract the fractions:

$\frac{9}{8} - \frac{4}{8} = \frac{5}{8}$

Combine the results:

$0 + \frac{5}{8} = \frac{5}{8}$

So, Sharyn will have $\frac{5}{8}$ yards of fabric left over. This final calculation is the answer we've been working towards. It shows how much extra fabric Sharyn has after making both dresses. Double-checking your work is always a good idea, especially in multi-step problems like this, to ensure you haven't made any small errors along the way.

Final Answer

After all the calculations, we've arrived at our final answer! Sharyn will have $\frac{5}{8}$ yards of fabric left over after making the dresses for herself and her daughter. Isn't it satisfying to solve a problem like this step by step? It shows how we can use math in everyday situations, like figuring out fabric needs for a sewing project. Understanding fractions and mixed numbers is super useful in many practical scenarios, and this problem is a great example of that. So, next time you're working on a project that involves measurements, remember these steps, and you'll be able to calculate everything you need with confidence!

Why This Matters: Real-World Applications

You might be wondering, why is this kind of math problem important? Well, think about all the times you encounter measurements and fractions in your daily life. This isn't just about dresses; it's about developing skills that are useful in a variety of situations. Whether you're cooking, doing home renovations, or working on any kind of craft project, understanding how to work with fractions and mixed numbers is essential. Imagine you're doubling a recipe that calls for $1 \frac{1}{2}$ cups of flour – you'll need to know how to multiply mixed numbers! Or, if you're building a bookshelf and need to cut a piece of wood to a specific length, you'll be using fractions and measurements. Mastering these math skills gives you the confidence to tackle these real-world challenges. Plus, it's not just about practical skills; it's also about developing your problem-solving abilities. Breaking down a complex problem into smaller, manageable steps, as we did with Sharyn's fabric problem, is a valuable skill that can be applied in many areas of life.

Tips for Tackling Similar Problems

When you encounter similar math problems involving fractions, mixed numbers, and real-world scenarios, there are a few key strategies that can help you tackle them with confidence. First and foremost, read the problem carefully. Make sure you understand exactly what the question is asking and what information you're given. Highlight the important numbers and keywords. Next, break the problem down into smaller steps, just like we did with Sharyn's fabric. Identify the operations you need to perform – whether it's addition, subtraction, multiplication, or division – and tackle them one at a time. When working with fractions, remember the importance of finding a common denominator. This is crucial for both addition and subtraction. And finally, always double-check your work. It's easy to make a small mistake along the way, so taking the time to review your calculations can save you from errors. Practice makes perfect, so the more you work with these types of problems, the more comfortable and confident you'll become.

Conclusion

So, there you have it! We've successfully solved Sharyn's fabric problem and learned some valuable skills along the way. By breaking the problem down into steps, we were able to add and subtract mixed numbers to find the amount of fabric Sharyn had left over. Remember, math isn't just about numbers and equations; it's about solving real-world problems and developing critical thinking skills. Whether you're planning a sewing project, cooking a meal, or tackling a home improvement task, the math skills you've learned here will come in handy. Keep practicing, keep exploring, and most importantly, keep having fun with math! Who knew fabric and fractions could be so interesting?