Verified answer

Answer:

12/56  

Step-by-step explanation:

The additive inverse of a number N is -N. Thus a number added to its additive inverse will be 0
N + (-N) = 0

Step 1:

Find the result of
[tex]-\frac{3}{8} - (-\frac{2}{7} )[/tex][tex]-\frac{21}{56} - (-\frac{16}{56} )[/tex]

= [tex]-\frac{21}{56} - (-\frac{16}{56} )[/tex]    making denominator equal and adjusting numerator

= [tex]-\frac{21}{56} + \frac{16}{56}[/tex]

= [tex]\frac{-21 + 16}{56}[/tex] = [tex]-\frac{5}{56}[/tex]  (1)

Step 2:

Find the inverse of [tex]-\frac{5}{56}[/tex]. This is [tex]\frac{5}{56}[/tex] (2)

Step 3

Find the sum of  [tex]\frac{1}{4} and -\frac{3}{8}[/tex]
[tex]\frac{1}{4} + (-\frac{3}{8})[/tex]  = [tex]\frac{1}{4} - \frac{3}{8}[/tex] = [tex]\frac{2}{8} - \frac{3}{8}[/tex] = [tex]\frac{1}{8}[/tex] (3)

Step 4

(2) - (3) ==> [tex]\frac{5}{56} - (-\frac{1}{8}) \\= \frac{5}{56} + \frac{1}{8} \\\\= \frac{5}{56} + \frac{7}{56}) \\\\= \frac{12}{56} or \frac{3}{14}[/tex]