To determine which pair of numbers, when multiplied together, gives the lowest product, we must evaluate the products of all possible pairs from the given set of numbers [tex]\(-5\)[/tex], [tex]\(-8\)[/tex], [tex]\(4\)[/tex], and [tex]\(9\)[/tex].
1. First, consider the pair [tex]\((-5, -8)\)[/tex]:
[tex]\[
(-5) \times (-8) = 40
\][/tex]
2. Next, consider the pair [tex]\((-5, 4)\)[/tex]:
[tex]\[
(-5) \times 4 = -20
\][/tex]
3. Then, consider the pair [tex]\((-5, 9)\)[/tex]:
[tex]\[
(-5) \times 9 = -45
\][/tex]
4. Now, consider the pair [tex]\((-8, 4)\)[/tex]:
[tex]\[
(-8) \times 4 = -32
\][/tex]
5. Next, consider the pair [tex]\((-8, 9)\)[/tex]:
[tex]\[
(-8) \times 9 = -72
\][/tex]
6. Finally, consider the pair [tex]\((4, 9)\)[/tex]:
[tex]\[
4 \times 9 = 36
\][/tex]
By comparing all these results:
- 40
- -20
- -45
- -32
- -72
- 36
The smallest (i.e., lowest) product is [tex]\(-72\)[/tex].
Hence, the pair of numbers that results in the lowest product is [tex]\((-8, 9)\)[/tex], and their product is [tex]\(-72\)[/tex].
