We are given the improper fraction
[tex]-\frac{11}{4}[/tex]And told to express it as a mixed number. To do so, we take the denominator (4) and look for the closes multiple of it that is less than the numerator (11).Then, we write the numerator as the sum of that multiple of the denominator and another number.
In this case, note that 4*2 = 8 and 4*3=12. So 8 is the multiple of 4 that is the closest to 11, such that it is less than 11.
In this case, we can write the following
[tex]\frac{11}{4}=\frac{8+3}{4}[/tex]Then, we can split the sum as follows
[tex]\frac{8+3}{4}=\frac{8}{4}+\frac{3}{4}=2+\frac{3}{4}[/tex]We see that there is one number that is not a fraction. This is the whole number of the mixed number. So we have
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Finally, we add the negative sign, so we get
[tex]-\frac{11}{4}=-2\frac{3}{4}[/tex]