luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice . she gives 5/8 cup of juice to mags . how much is left in luna glass

Answer:[tex]\frac{1}{2}[/tex]Step-by-step explanation:We have been given that Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice.First of all, let us find the total amount of juice Luna had by adding the amount of orange juice to amount of cranberry juice.[tex]\text{Total amount of juice Luna had}=\frac{3}{4}+\frac{3}{8}[/tex]Let us have a common denominator.[tex]\text{Total amount of juice Luna had}=\frac{3\times 2}{4\times 2}+\frac{3}{8}[/tex][tex]\text{Total amount of juice Luna had}=\frac{6}{8}+\frac{3}{8}[/tex][tex]\text{Total amount of juice Luna had}=\frac{6+3}{8}[/tex][tex]\text{Total amount of juice Luna had}=\frac{9}{8}[/tex]Since Luna gave 5/8 cup of juice to Mags, so let us subtract amount of juice given to Mags from the total amount of juice to find the amount of juice left in Luna's glass.[tex]\text{Amount of juice left in Luna's glass}=\frac{9}{8}-\frac{5}{8}[/tex][tex]\text{Amount of juice left in Luna's glass}=\frac{9-5}{8}[/tex][tex]\text{Amount of juice left in Luna's glass}=\frac{4}{8}[/tex][tex]\text{Amount of juice left in Luna's glass}=\frac{1}{2}[/tex]Therefore, the amount of  juice left in Luna's glass is [tex]\frac{1}{2}[/tex].