Absolutely, let's solve these questions step by step.
3. Write the additive inverse of [tex]\(\frac{9}{11}\)[/tex].
When we talk about the additive inverse, we refer to a number which, when added to the original number, results in zero. For any number [tex]\(a\)[/tex], the additive inverse is [tex]\(-a\)[/tex].
For the fraction [tex]\(\frac{9}{11}\)[/tex], the additive inverse is:
[tex]\[
-\frac{9}{11} \approx -0.8181818181818182
\][/tex]
4. Write the multiplicative inverse of [tex]\(-\frac{5}{12}\)[/tex].
When we talk about the multiplicative inverse, we refer to a number which, when multiplied by the original number, results in one. For any nonzero number [tex]\(a\)[/tex], the multiplicative inverse is [tex]\(\frac{1}{a}\)[/tex].
For the fraction [tex]\(-\frac{5}{12}\)[/tex], the multiplicative inverse is:
[tex]\[
-\frac{12}{5} \approx -2.4
\][/tex]
5. Fill in the blank and write the name.
Let's fill in the blank based on the inverses we have calculated:
- The additive inverse of [tex]\(\frac{9}{11}\)[/tex] is approximately [tex]\(-0.8181818181818182\)[/tex].
- The multiplicative inverse of [tex]\(-\frac{5}{12}\)[/tex] is [tex]\(-2.4\)[/tex].
In summary:
- The additive inverse of [tex]\(\frac{9}{11}\)[/tex] is [tex]\(-\frac{9}{11}\)[/tex].
- The multiplicative inverse of [tex]\(-\frac{5}{12}\)[/tex] is [tex]\(-\frac{12}{5}\)[/tex].
