Question

Evaluate the expression. \(-\frac{7}{9}+\frac{1}{3}+2\)

Short answer

The answer to the expression is \(\frac{14}{9}\), or alternatively, \(1\frac{5}{9}\).

Step-by-step solution

Identify Like Fractions

Identify the fractions that have the same denominator (i.e., \(-\frac{7}{9}\) and \(\frac{1}{3}\)) and convert any fractions with a different denominator to an equivalent fraction with the common denominator. In this case, convert \(\frac{1}{3}\) to \(\frac{3}{9}\) as 1/3 is equivalent to 3/9.

Add/Subtract Like Fractions

Add or subtract fractions with like denominators by adding or subtracting the numerators and keeping the denominator the same. Here, subtract \(\frac{7}{9}\) and \(\frac{3}{9}\) to get \(-\frac{4}{9}\).

Add Integer

A whole number can be treated as a fraction with a denominator of 1. So, add the fraction \(-\frac{4}{9}\) to the whole number \(2\) (or \(\frac{18}{9}\)) to get \(\frac{14}{9}\).