Answer:
[tex]\large\boxed{m=10.8=10\dfrac{4}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{5}{8}m=6\dfrac{3}{4}\qquad\text{convert the mixed number to an improper fraction}\\\\\dfrac{5m}{8}=\dfrac{6\cdot4+3}{4}\\\\\dfrac{5m}{8}=\dfrac{27}{4}\qquad\text{cross multiply}\\\\(5m)(4)=(8)(27)\\\\20m=216\qquad\text{divide both sides by 20}\\\\\dfrac{20m}{20}=\dfrac{216}{20}\\\\m=10.8[/tex]
[tex]\bold{Check:}\\\\\dfrac{5}{8}\cdot10.8=\dfrac{5\!\!\!\!\diagup^1}{8}\cdot\dfrac{108}{10\!\!\!\!\!\diagup_2}=\dfrac{108:4}{16:4}=\dfrac{27}{4}=\dfrac{24+3}{4}=\dfrac{24}{4}+\dfrac{3}{4}=6\dfrac{3}{4}\\\\\bold{CORRECT}[/tex]
