List the partial products of 242 and 28.
The Correct Answer and Explanation is :
To find the partial products of 242 and 28, we can break down each number by place value and use the distributive property to calculate the result. Here’s the step-by-step process:
- Break down the numbers by place value:
- 242 = 200 + 40 + 2
- 28 = 20 + 8
- Multiply each part (partial product):
- (200 \times 20 = 4000)
- (200 \times 8 = 1600)
- (40 \times 20 = 800)
- (40 \times 8 = 320)
- (2 \times 20 = 40)
- (2 \times 8 = 16)
- List of partial products:
- 4000
- 1600
- 800
- 320
- 40
- 16
- Add all the partial products to find the final answer:
- (4000 + 1600 + 800 + 320 + 40 + 16 = 6776)
So, 242 multiplied by 28 equals 6776.
Explanation
Using partial products to multiply is a technique that involves breaking down numbers into parts based on their place values. This method allows us to simplify complex multiplication by handling smaller, more manageable multiplications.
For example, instead of multiplying 242 by 28 directly, we separate the values into hundreds, tens, and units. We then multiply each part of the first number (242) by each part of the second number (28). This generates partial products, which are easier to work with individually. Finally, we add all the partial products to obtain the final answer.
This method illustrates the distributive property of multiplication over addition, where (a \times (b + c) = (a \times b) + (a \times c)). This approach is especially useful when dealing with large numbers in mental math or in situations where a calculator is not available, and it helps reinforce an understanding of place value and basic arithmetic.