Distributive Property: Solve 7 X 9 Step-by-Step

Hey guys! Let's break down how to solve 7 x 9 using the distributive property. It might sound intimidating, but it's actually a super useful trick in mathematics. We'll go through it step by step, so you can totally master this concept. We will solve the expression 7 x 9 by using 7 x (5 + 4), and we will fill in the blanks to complete the equation.

Understanding the Distributive Property

Before we dive into the problem, let's quickly recap what the distributive property is all about. In simple terms, it allows us to multiply a number by a sum (or difference) by multiplying the number by each term inside the parentheses separately and then adding (or subtracting) the results. The formula looks like this: a × (b + c) = (a × b) + (a × c). This property is a foundational concept in algebra and arithmetic, making it easier to handle complex calculations by breaking them down into simpler parts. Mastering it not only helps in solving numerical problems but also provides a strong base for algebraic manipulations and equation-solving. The distributive property showcases how multiplication interacts with addition and subtraction, offering a flexible approach to calculations and a deeper insight into mathematical operations.

This property is especially handy when dealing with larger numbers or algebraic expressions. It allows you to simplify calculations by breaking them down into smaller, more manageable parts. For instance, instead of directly multiplying 7 by 9, we can decompose 9 into a sum that’s easier to work with, like 5 + 4. This method not only makes mental calculations easier but also reduces the chances of errors when working with pen and paper. The distributive property bridges the gap between basic arithmetic and more advanced algebraic concepts, making it an indispensable tool in mathematical problem-solving.

Applying the distributive property is not just about finding the right answer; it’s also about understanding the underlying mathematical structure. It encourages a flexible mindset when approaching problems, allowing you to see numbers and expressions in different ways. This is particularly beneficial in higher mathematics, where problems often require creative manipulation and simplification. Moreover, it helps in visualizing mathematical relationships, making abstract concepts more concrete and understandable. By mastering the distributive property, you're not just learning a mathematical trick, you're developing a more profound understanding of how numbers interact with each other, which is invaluable for your mathematical journey.

Solving 7 x 9 using the Distributive Property

Okay, let's get down to business and solve 7 x 9 using the distributive property. The key here is to rewrite 9 as a sum of two numbers that are easy to multiply by 7. We'll use 5 and 4 because they are straightforward to work with, but remember there can be other numbers we can use, but for now let's stick to these numbers. So, we can rewrite 9 as 5 + 4. Now our problem looks like this: 7 x (5 + 4).

This is where the distributive property comes into play. We're going to distribute the 7 across both the 5 and the 4. This means we'll multiply 7 by 5 and then multiply 7 by 4. Think of it like this: we're giving the 7 to both numbers inside the parentheses. So, we get (7 x 5) + (7 x 4). See how we've broken down the original problem into two smaller multiplication problems? This is the power of the distributive property in action!

Now, let's solve those smaller problems. 7 multiplied by 5 is 35, and 7 multiplied by 4 is 28. So, our expression becomes 35 + 28. The final step is super simple: we just add 35 and 28 together. If you do the math, you'll find that 35 + 28 equals 63. And guess what? That's the answer to 7 x 9! By using the distributive property, we were able to solve a multiplication problem by breaking it down into simpler steps. This not only makes the problem easier to manage but also deepens our understanding of how multiplication and addition work together. So next time you're faced with a tough multiplication, remember the distributive property – it's your mathematical superpower!

Step-by-Step Breakdown: Filling in the Blanks

Now, let's go through the problem step-by-step, just like the one you might see in a worksheet or textbook. This will help solidify your understanding and make sure you can tackle similar problems with confidence. We’ll fill in the blanks to complete the equation, making each step crystal clear.

We start with our original problem: 7 x 9. The first step is to rewrite 9 as a sum. As we discussed earlier, we'll use 5 + 4. So, the first blank we need to fill is: 7 x (5 + 4). This sets the stage for applying the distributive property. Remember, we're not changing the value of the expression; we're just rewriting it in a way that makes it easier to work with. This is a common strategy in math – transforming a problem into an equivalent form that's simpler to solve.

Next, we apply the distributive property. This means we multiply 7 by both 5 and 4 separately. So, we get (7 x 5) + (7 x 4). This is the second blank we need to fill. Notice how we've distributed the 7 across both numbers inside the parentheses. This is the heart of the distributive property, and it's crucial to get this step right. By breaking the problem into two smaller multiplications, we've made it much more manageable.

Now, let's solve the individual multiplications. 7 x 5 equals 35, and 7 x 4 equals 28. So, the next part of our equation is 35 + 28. This corresponds to the third blank. We're almost there! We've simplified the problem down to a simple addition. This is a great example of how the distributive property can turn a more complex problem into easier steps.

Finally, we add 35 and 28 together. As we found earlier, 35 + 28 equals 63. So, the last blank we fill is 63. We've done it! We've successfully used the distributive property to solve 7 x 9, and we've filled in all the blanks along the way. By breaking down the problem step-by-step, we've not only found the answer but also reinforced our understanding of the distributive property. Remember, practice makes perfect, so try this method with other multiplication problems to become a distributive property pro!

Practice Makes Perfect

The best way to truly understand the distributive property is to practice it! Try solving other multiplication problems using this method. For instance, you could try breaking down 8 x 6 or 9 x 7. Remember, the key is to rewrite one of the numbers as a sum (or difference) of two other numbers. Don't be afraid to experiment with different combinations – the more you practice, the more comfortable you'll become with this powerful mathematical tool. Also, try creating your own problems and solving them using the distributive property. This will not only help you master the technique but also deepen your understanding of how numbers work together.

Another great way to practice is to look for real-world examples where you can apply the distributive property. For example, if you're buying several items at a store and each item costs the same amount, you can use the distributive property to calculate the total cost. Or, if you're planning a party and need to figure out how many snacks to buy, you can use it to simplify the calculations. By seeing how the distributive property applies to everyday situations, you'll appreciate its usefulness even more. So, keep practicing, keep experimenting, and soon you'll be a master of the distributive property!

Conclusion

So there you have it, guys! We've successfully solved 7 x 9 using the distributive property. We learned how to break down a multiplication problem into smaller, more manageable steps by rewriting one of the numbers as a sum. We also filled in the blanks to clearly see each step of the process. Remember, the distributive property is a powerful tool in mathematics, and with practice, you'll become a pro at using it. Keep practicing, and you'll be amazed at how much easier multiplication problems can become! This method not only helps you find the answer but also deepens your understanding of mathematical principles. Keep up the great work, and you'll be solving even more complex problems in no time! Happy calculating!