Subtract the following two fractions

Explanation

Add the opposite of \(-\frac23\), which is \(\frac23\)

$-\frac73 - \left( -\frac23 \right) = -\frac7d + \frac23$

Write \(-\frac73 as \frac{-7}{3}\)

$= \frac{-7}{3} + \frac23$

Add the numerators and write the sum over the common denominator 3

$= \frac{-7 + 2}{3}$

Use the rule for adding two integers with different signs: -7 + 2 = -5

$=\frac{-5}{3}$

Rewrite the result with the - sign in format: \(\frac{-5}{3} = -\frac53\).  This fraction is in simplest form

$=-\frac53$