Answer:
[tex]\frac{119}{120}\ gal[/tex]
Step-by-step explanation:
we know that
The algebraic expression to find out how many gallons of paint he will have left after painting the mural is equal to
[tex](1\frac{1}{5}-\frac{3}{4}) + (1\frac{1}{6}-\frac{3}{4})+(\frac{7}{8}-\frac{3}{4})[/tex]
Convert mixed numbers to an improper fractions
[tex]1\frac{1}{5}=1+\frac{1}{5}=\frac{1*5+1}{5}=\frac{6}{5}[/tex]
[tex]1\frac{1}{6}=1+\frac{1}{6}=\frac{1*6+1}{6}=\frac{7}{6}[/tex]
substitute
[tex](\frac{6}{5}-\frac{3}{4}) + (\frac{7}{6}-\frac{3}{4})+(\frac{7}{8}-\frac{3}{4})[/tex]
Find the least common multiple (LCM) for the denominators
[tex](\frac{4*6-3*5}{20}) + (\frac{2*7-3*3}{12})+(\frac{7-3*2}{8})[/tex]
[tex](\frac{9}{20}) + (\frac{5}{12})+(\frac{1}{8})[/tex]
Find the least common multiple (LCM) for the denominators
The LCD is
[tex](2^3)(3)(5)=120[/tex]
[tex](\frac{9*6+5*10+1*15}{120})[/tex]
[tex]\frac{119}{120}\ gal[/tex]
