Use a different integer 1, 2, 3, or 4 for each of a, b, c,
and d in the multiplication sentence a/b x c/d to make
the greatest possible product.
Where would I put the four integers 5, 6, 7, and 8 to make the greatest possible product?
But then how would I put 2, 5, 8, and 9?
I need a description of the pattern in the placement of the integers that generates the greatest
product.
PUt the greatest integers in the numerators, and the lessor integers in the denominators.
7x8/6x5 or 7/6 * 8/5
5my square
To find the arrangement that generates the greatest possible product, follow these steps:
1. Start with the given integers and the multiplication sentence "a/b x c/d".
2. Arrange the integers in descending order, from the largest to the smallest. For example, in the case of 5, 6, 7, and 8, the descending order would be 8, 7, 6, 5.
3. To place the integers in the multiplication sentence, assign the largest integer to the numerator (a) and the second-largest integer to the denominator (b). Then, assign the third-largest integer to the other numerator (c) and the smallest integer to the other denominator (d).
4. In this case, the arrangement that generates the greatest possible product would be 8/7 x 6/5.
If you were given the integers 2, 5, 8, and 9, you would follow the same steps:
1. Arrange the integers in descending order: 9, 8, 5, 2.
2. Assign the largest integer (9) to the numerator (a) and the second-largest integer (8) to the denominator (b). Then, assign the third-largest integer (5) to the other numerator (c) and the smallest integer (2) to the other denominator (d).
3. The arrangement that generates the greatest possible product would be 9/8 x 5/2.
In general, the pattern in the placement of the integers that generates the greatest product is to assign the largest number to the numerator and the second-largest to the denominator, then assign the third-largest to the other numerator and the smallest to the other denominator. This arrangement ensures that the largest numbers are multiplied together and the smallest numbers are multiplied together, resulting in a greater overall product.