Distributive Property: Solving $7 imes 8 rac{4}{5}$

Oct 23, 2025 by SD Solar 54 views

Distributive Property: Breaking Down $7 imes 8 rac{4}{5}$

Hey everyone! Today, we're diving into the distributive property and how it helps us solve multiplication problems, specifically $7 imes 8 rac{4}{5}$ . Don't worry, it's not as scary as it sounds! The distributive property is a super useful tool that makes complex calculations much easier to handle. It's like having a secret weapon in your math arsenal. We'll break down the problem step-by-step, making sure you understand the 'why' behind each move. So, let's get started and see how we can apply this awesome property! This particular problem is a classic example of how the distributive property can simplify multiplying a whole number by a mixed number. Instead of directly tackling the mixed number, we'll use the distributive property to break it down into smaller, more manageable parts. By the end of this, you will be able to solve similar problems with confidence.

Understanding the Distributive Property

Alright, first things first, what exactly is the distributive property? Simply put, it's a rule that allows us to multiply a number by a sum or difference by multiplying that number by each term inside the parentheses separately and then adding the products. In a more mathematical way, for any numbers a, b, and c: a × (b + c) = (a × b) + (a × c). Think of it like sharing: you're distributing the multiplication across each part of the sum. Now, let's look at our problem, $7 imes 8 rac{4}{5}$ . We have a whole number (7) multiplied by a mixed number ( $8 rac{4}{5}$ ). This is where the distributive property shines. First, we need to rewrite the mixed number as a sum. We can rewrite $8 rac{4}{5}$ as $8 + rac{4}{5}$ . This is a crucial step! By doing this, we can now apply the distributive property.

We'll then multiply the whole number (7) by each part of the sum separately: $7 imes 8$ and $7 imes rac{4}{5}$ . Finally, we'll add the results together. This will give us the answer. This method makes the calculation much simpler. It reduces the chance of making errors. This approach is much more accessible than trying to directly multiply with the mixed number. The distributive property transforms what seems like a complex problem into a series of easier steps. This is the essence of why this property is so powerful. It breaks down complex problems into more manageable ones.

By understanding this, you're not just learning to solve one problem. You're learning a versatile technique applicable to many situations. Remember the equation: a × (b + c) = (a × b) + (a × c). This is the key. Keep this equation in mind. It's your guide to using the distributive property. Practice with different numbers and problems. The more you practice, the more comfortable you'll become with this useful tool.

Applying the Distributive Property to $7 imes 8 rac{4}{5}$

Okay, let's get down to the actual calculation. Here’s how we'll use the distributive property to solve $7 imes 8 rac{4}{5}$ . Remember, $8 rac{4}{5}$ is the same as $8 + rac{4}{5}$ . So our problem becomes $7 imes (8 + rac{4}{5})$ . Now, using the distributive property, we multiply 7 by each term inside the parentheses: First, multiply 7 by 8: $7 imes 8 = 56$ . Second, multiply 7 by $rac{4}{5}$ : $7 imes rac{4}{5} = rac{28}{5}$ . Now, we add the two results together: $56 + rac{28}{5}$ . Here, we can convert the fraction $rac{28}{5}$ into a mixed number to make the addition easier. $rac{28}{5}$ is equal to $5 rac{3}{5}$ . So, our expression is now $56 + 5 rac{3}{5}$ . Finally, add 56 and $5 rac{3}{5}$ : $56 + 5 rac{3}{5} = 61 rac{3}{5}$ . And there you have it! The answer to $7 imes 8 rac{4}{5}$ using the distributive property is $61 rac{3}{5}$ . Isn't that neat? By breaking the problem down, we made the calculation much easier to solve.

We could have also chosen the wrong way, which is to convert $8 rac{4}{5}$ into an improper fraction first. Then multiply. But by doing this we're adding additional steps and increasing the chances for error. So, the distributive property not only simplifies the calculation, but it also reduces the likelihood of making mistakes. This method is incredibly useful. It allows us to approach complex problems more confidently. Remember, the key is to break down the mixed number, distribute the multiplication, and then add the results. Practice these steps. You will be able to master the distributive property in no time. The more you use it, the more familiar it will become, making math problems less daunting and more enjoyable to solve.

Analyzing the Answer Choices

Now, let's analyze the given answer choices to see which one correctly demonstrates the use of the distributive property for the problem $7 imes 8 rac{4}{5}$ .

Option A: $56+ rac{28}{5}=56+5 rac{3}{5}=61 rac{3}{5}$ This option is the correct one. It perfectly shows the application of the distributive property. First, it multiplies 7 by 8, which results in 56. Then, it multiplies 7 by $rac{4}{5}$ , giving us $rac{28}{5}$ . It then converts $rac{28}{5}$ into a mixed number ( $5 rac{3}{5}$ ). Finally, it adds 56 and $5 rac{3}{5}$ to arrive at the correct answer, $61 rac{3}{5}$ . This is a clear and accurate demonstration of the distributive property. It shows how the mixed number is broken down, and the multiplication is distributed across its components.
Option B: $56 imes rac{28}{5}= rac{1568}{5}=313 rac{3}{5}$ This option is incorrect because it does not correctly apply the distributive property. It appears to multiply 56 by $rac{28}{5}$ . This is not the correct approach. It doesn't break down the mixed number as the distributive property requires. Instead, it seems to have an incorrect setup and therefore produces a wrong answer. This method doesn't follow the proper steps for using the distributive property. So, this option is not the right choice for demonstrating how the distributive property is used.

To reiterate, the distributive property involves multiplying the whole number by each part of the mixed number (after breaking it down) separately and then adding the results. Option A correctly represents these steps. Option B fails to do so. Therefore, the right answer is Option A, because it precisely mirrors the process of using the distributive property to solve the original problem.

Conclusion: Mastering the Distributive Property

And that's a wrap, folks! We've successfully used the distributive property to solve $7 imes 8 rac{4}{5}$ . Remember, the distributive property is a powerful tool. It's all about breaking down a complex problem into smaller, simpler parts. By understanding this, you can tackle more difficult math problems with confidence. Keep practicing. The more you use it, the easier and more natural it will become. Don't be afraid to experiment with different numbers and problems. This will solidify your understanding and boost your problem-solving skills.

Always remember to rewrite the mixed number as a sum. Distribute the multiplication, and add the results. That's the key to mastering the distributive property. This property isn't just useful for this specific problem. It's a fundamental concept that you'll encounter throughout your math journey. So, understanding it well is an investment in your mathematical future. Keep up the great work. Math can be enjoyable if you approach it with the right tools and mindset. You got this, guys! Keep practicing, and you'll become a distributive property pro in no time! Remember to always break down complex problems into manageable steps. This will make your math journey smoother and more successful. Happy calculating!