lliana’s math grade increased from 65 to 86. Fiona’s math grade increased from 70 to 80. What is the difference, rounded to the nearest whole number, between the approximate percent increases?

Okay. Let us do it surgically. Let us solve first the rate of increase in Lliana's Math grade. 86-65 = 21, thus the rate can be written as a fraction 21/65. We will reserve the decimal form once we are done with both rates of increase.

On the same note, Fiona's increase in Math grade is determined by subtracting 70 from her recent grade of 80, thus giving us an increase in her grade by 10. Therefore, the rate of increase in her Math grade is 10/70.

Now, let us take the decimal forms of the students' grade in math respectively. Lliana's is 21/65 or 0.32307692307... Fiona's is 10/70 or 0.14285714285. Now, subtracting this decimals we have 0.18021978021.
Changing it to percent form, we must multiply it by 100 and add the symbol "%". Therefore, we have 18.021978021 %.

Finally, rounding the value to the nearest whole number, we obtained 18.00% or just 18%.