# Explain Why It Works to Break Apart a Number by Place Values to Multiply

Explain Why It Works to Break Apart a Number by Place Values to Multiply

When we first learn multiplication, it can seem like a daunting task to multiply large numbers. However, breaking apart a number by its place values can significantly simplify the process and make multiplication much easier to understand. In this article, we will explore why breaking apart a number by place values works when multiplying and how it can help us solve complex multiplication problems with ease.

To understand why breaking apart a number by place values works, let’s first revisit the concept of place values. In our decimal number system, each digit in a number represents a specific value based on its position. The rightmost digit is in the ones place, the next digit is in the tens place, followed by the hundreds place, and so on. Breaking a number apart by its place values means separating each digit into its respective place value.

Now, let’s consider a simple multiplication problem: 23 multiplied by 5. Instead of multiplying the two numbers directly, we can break apart 23 into its place values. In this case, 23 can be represented as 20 + 3. Now, we multiply each part separately. 20 multiplied by 5 is 100, and 3 multiplied by 5 is 15. Finally, we add these two results together: 100 + 15 = 115. Therefore, 23 multiplied by 5 equals 115.

Breaking apart the number by place values allows us to multiply each part individually, making the calculation easier to manage. When we add the products of each part, we obtain the final result. This method works because of the distributive property of multiplication, which states that multiplying a number by the sum of two other numbers is the same as multiplying the number by each of those two numbers separately and then adding the products together.

Let’s further explore this concept with a more complex example. Consider the multiplication problem 365 multiplied by 8. Breaking down 365 by place values, we have 300 + 60 + 5. Now, we multiply each part separately: 300 multiplied by 8 is 2400, 60 multiplied by 8 is 480, and 5 multiplied by 8 is 40. Adding these three results together, we get 2400 + 480 + 40 = 2920. Therefore, 365 multiplied by 8 equals 2920.

Breaking apart the number by place values allows us to handle larger numbers with ease. Instead of trying to multiply a three-digit number by another three-digit number, we can break each number down into its respective place values and multiply them separately. This method not only simplifies the calculation process but also helps us understand the underlying principles of multiplication.

FAQs:

Q: Can this method be used for any multiplication problem?
A: Yes, this method can be used for any multiplication problem, regardless of the size of the numbers involved. Breaking apart numbers by their place values can make multiplication easier and more manageable.

Q: Are there any limitations to this method?
A: While breaking apart numbers by place values is a useful technique for multiplication, it may not always be the most efficient method for certain calculations. In some cases, mental math or other strategies may be more suitable.

Q: Is breaking apart numbers by place values the only way to solve multiplication problems?
A: No, there are multiple methods to solve multiplication problems. Breaking apart numbers by place values is just one approach that can simplify the calculation process and enhance understanding.