Final answer:
To solve for k in the equation 9 and 1/12 = k/9, convert the mixed number to an improper fraction and then cross-multiply and divide to isolate k, resulting in k = 81.75.
Step-by-step explanation:
To solve the equation 9 and 1/12 = k/9, we first need to convert the mixed number to an improper fraction. The mixed number 9 and 1/12 can be converted by multiplying the whole number 9 by the denominator 12 and adding the numerator 1, which gives us 109/12.
Now the equation looks like this: 109/12 = k/9. To find the value of k, we cross-multiply which gives us 109 * 9 = 12 * k. When we do the multiplication, we get 981 = 12k.
To isolate k, we then divide both sides by 12. So, k = 981/12. Simplifying this, we get k = 81.75.