Questions: Evaluate the expression shown below and write your answer as a fraction in simplest form. -9/8 + 6/11

Solution Steps

To evaluate the expression \(-\frac{9}{8}+\frac{6}{11}\), we need to find a common denominator for the fractions. Once we have a common denominator, we can add the numerators and simplify the resulting fraction to its simplest form.

We start with the expression \(-\frac{9}{8} + \frac{6}{11}\). The fractions involved are \(-\frac{9}{8}\) and \(\frac{6}{11}\).

To add the fractions, we need a common denominator. The denominators are 8 and 11, so the least common denominator is \(8 \times 11 = 88\).

Convert each fraction to have the common denominator of 88:

• \(-\frac{9}{8} = -\frac{9 \times 11}{8 \times 11} = -\frac{99}{88}\)
• \(\frac{6}{11} = \frac{6 \times 8}{11 \times 8} = \frac{48}{88}\)

Add the numerators of the fractions: \[ -\frac{99}{88} + \frac{48}{88} = \frac{-99 + 48}{88} = \frac{-51}{88} \]

The fraction \(\frac{-51}{88}\) is already in its simplest form since 51 and 88 have no common factors other than 1.

Final Answer