Evaluate the expression shown below and write ur answer as a fraction in simplest form. -9/4 / 4/3 + 11/4

Answer 1

To evaluate the expression \(-\frac{9}{4} \div \frac{4}{3} + \frac{11}{4}\), we will first handle the division and then the addition.

Step 1: Division \(-\frac{9}{4} \div \frac{4}{3}\)

Dividing by a fraction is equivalent to multiplying by its reciprocal:

\[ -\frac{9}{4} \div \frac{4}{3} = -\frac{9}{4} \times \frac{3}{4} \]

Now, we multiply the fractions:

\[ -\frac{9 \cdot 3}{4 \cdot 4} = -\frac{27}{16} \]

Step 2: Addition \(-\frac{27}{16} + \frac{11}{4}\)

To add these two fractions, we need a common denominator. The common denominator between \(16\) and \(4\) is \(16\).

Now, we will convert \(\frac{11}{4}\) to have a denominator of \(16\):

\[ \frac{11}{4} = \frac{11 \cdot 4}{4 \cdot 4} = \frac{44}{16} \]

We can now add the fractions:

\[ -\frac{27}{16} + \frac{44}{16} = \frac{-27 + 44}{16} = \frac{17}{16} \]

Conclusion

The final value of the expression is:

\[ \boxed{\frac{17}{16}} \]