Given the four rational numbers below, find the greatest difference and the greatest product using two of the numbers for each operation.
2 1/3,1.5, -1.25, -3 1/4
Difference= -0.95 is what I got for the first answer.
Product= 4.0925 is what I got for the second
you need to plot these values on the number line. You can see that the leftmost point is -3 1/4 and the rightmost is 2 1/3
Thus, the greatest difference is between them: 2 1/3 - (-3 1/4) = 5.583
If "greatest" product means its algebraic value, then any positive product i greater than all of the negative products. That makes (-1.25)(-3 1/4) = 4.0625
thank you!
My name is jagjeet singh
To find the greatest difference, you need to subtract two numbers and see which pair results in the largest absolute value. Here's how you can do it:
1. Find the absolute difference between each pair of numbers:
- Absolute difference between 2 1/3 and 1.5: |2 1/3 - 1.5| = 2 1/3 - 1.5 = 5/3 - 1.5 = 1/3
- Absolute difference between 2 1/3 and -1.25: |2 1/3 - (-1.25)| = 2 1/3 + 1.25 = 7/3 + 5/4
= 28/12 + 15/12 = 43/12 ≈ 3.583
- Absolute difference between 2 1/3 and -3 1/4: |2 1/3 - (-3 1/4)| = 2 1/3 + 3 1/4 = 7/3 + 13/4
= 28/12 + 39/12 = 67/12 ≈ 5.583
From the three absolute differences, the largest is 5.583, which is the greatest difference.
To find the greatest product, you need to multiply two numbers and find the pair with the largest product. Here's how you can do it:
1. Multiply each pair of numbers:
- Product of 2 1/3 and 1.5: (2 1/3) * 1.5 = 7/3 * 3/2 = 7/2 ≈ 3.5
- Product of 2 1/3 and -1.25: (2 1/3) * (-1.25) = 7/3 * (-5/4) = -35/12 ≈ -2.917
- Product of 2 1/3 and -3 1/4: (2 1/3) * (-3 1/4) = 7/3 * (-13/4) = -91/12 ≈ -7.583
Out of the three products, the largest is 3.5, which is the greatest product.
Therefore, the greatest difference is 5.583, and the greatest product is 3.5.