Let's solve this step-by-step, identifying the greatest sum, difference, product, and quotient from the six given rational numbers:
The given numbers are:
- [tex]\( -5 \frac{1}{2} = -5.5 \)[/tex]
- [tex]\( 3.75 \)[/tex]
- [tex]\( -20.8 \)[/tex]
- [tex]\( 8 \)[/tex]
- [tex]\( -4 \)[/tex]
- [tex]\( 11 \frac{1}{4} = 11.25 \)[/tex]
Greatest Sum:
To find the greatest sum, we need to identify the two largest numbers. The two largest numbers in the list are 11.25 and 8.
Greatest sum:
[tex]\[ 11.25 + 8 = 19.25 \][/tex]
Greatest Difference:
To find the greatest difference, we need to calculate the difference between the largest number and the smallest number. The largest number is 11.25 and the smallest is -20.8.
Greatest difference:
[tex]\[ 11.25 - (-20.8) = 11.25 + 20.8 = 32.05 \][/tex]
Greatest Product:
To find the greatest product, we need to identify the two largest absolute values, as the product of these numbers will yield the greatest magnitude. Here, the numbers with the greatest absolute values are 11.25 and 8.
Greatest product:
[tex]\[ 11.25 \times 8 = 90.0 \][/tex]
Greatest Quotient:
To find the greatest quotient, the strategy is to divide the number with the largest absolute value by the number with the next largest absolute value. The number with the highest absolute value is 20.8, and then the second-highest absolute value is 11.25. However, since 20.8 is negative and 11.25 is positive, this produces the greatest negative quotient.
Greatest quotient:
[tex]\[ -20.8 / 11.25 \approx -1.848888888888889 \][/tex]
Therefore, the results are:
- Greatest sum: [tex]\[
11.25 + 8 = 19.25
\][/tex]
- Greatest difference: [tex]\[
11.25 - (-20.8) = 32.05
\][/tex]
- Greatest product: [tex]\[
11.25 \times 8 = 90.0
\][/tex]
- Greatest quotient: [tex]\[
-20.8 / 11.25 \approx -1.848888888888889
\][/tex]
