Answer:
[tex]7\,\frac{3}{8}-\frac{4}{7} = 6\,\frac{45}{56}[/tex]
Step-by-step explanation:
Let [tex]x = 7\,\frac{3}{8}-\frac{4}{7}[/tex], we proceed to simplify into a single rational number by algebraic means:
1) [tex]7\,\frac{3}{8} -\frac{4}{7}[/tex] Given
2) [tex]\left(\frac{56}{8}+\frac{3}{8}\right)-\frac{4}{7}[/tex] Definition of mixed number/Associative property
3) [tex]\frac{59}{8}-\frac{4}{7}[/tex] [tex]\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}[/tex]
4) [tex]\frac{413-32}{56}[/tex] [tex]\frac{a}{b}+\frac{c}{d}[/tex]
5) [tex]\frac{381}{56}[/tex] Definition of subtraction
6) [tex]\frac{336}{56}+\frac{45}{56}[/tex] [tex]\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}[/tex]
7) [tex]6\,\frac{45}{56}[/tex] Definition of mixed number/Result
