Using the following six digits, 1, 2, 4, 6, 8, and 9, fill in the blanks below to make the maximum product that you can. Use each digit only once. How does an understanding of place value help determine the best solution to this problem?
__ __ __ x __ __ __
In general, the digits inside of each number should be descending from left to right, since the left-most digits have a multiplier of 100.
So 8 and 9 occupy the left-most digits, and 4 and 6 the second.
Pair 4 with the greater digit, i.e. 9, and 6 with the smaller (8).
Proceed this way for the right-most digits.
Post what you've got if you wish.
941 x 862
To determine the best solution for this problem, we need to maximize the product by placing the digits in the correct positions. Understanding place value helps us determine the value of each digit in its respective position.
To find the maximum product, we want to place the largest digits in the positions with the highest value. Since the ones place has the lowest value, we'll put the largest digit there. Similarly, the tens place has a higher value than the ones place, so we'll put the second-largest digit there. Continuing this pattern, we'll place the remaining digits in descending order.
Therefore, the best solution to maximize the product is:
9 8 6 x 4 2 1
To find the best possible solution and maximize the product, you need to consider the place value of each digit. The higher the place value, the more it contributes to the overall product.
In this case, we want to maximize the product, so it makes sense to put the highest digits in the higher place values. This way, they have a greater impact on the product.
Let's break it down:
First, identify the highest available digit, which is 9. Since we want to maximize the product, it would be logical to place 9 in the thousands place.
Now, we are left with the remaining five digits: 1, 2, 4, 6, and 8.
Next, we need to consider the next highest available digit, which is 8. Since we've placed the 9 in the thousands place, we can now place the 8 in the hundreds place.
Now, we are left with four digits: 1, 2, 4, and 6.
To maximize the product, it would be ideal to place the remaining digits in increasing order.
So, continuing in this manner, we would place 6 in the tens place, followed by 4 in the ones place, 2 in the ten-thousandths place, and 1 in the hundred-thousandths place.
The final arrangement would be:
9 8 6 x 4 2 1
By arranging the digits in this way, with the highest digits in the highest place values, we can determine the best solution and achieve the maximum product.