Answer:
[tex]\frac{33}{44} =0.825[/tex]
Step-by-step explanation:
so for this, I'm going to start with the left side because it's easier
when multiplying fraction you go straight across
[tex]\frac{2}{5} *\frac{1}{2} =\frac{2}{10}=\frac{1}{5}[/tex] I simplified the fraction by recognizing 2 goes into both 2 and 10
now lets move on to the right side this is where it gets more complicated so to start lets turn that mixed fraction into an improper faction so to convert that you do:
the whole number multiplied by the denominator plus the numerator to get your mixed fraction numerator
1*5+1= 6 so the improper fraction is [tex]\frac{6}{5}[/tex]
when dividing by fraction you flip the second fraction and then multiply also known as multiplying by the reciprocal
[tex]\frac{3}{4} *\frac{5}{6}[/tex] now we do the same thing as before multiply straight across
[tex]\frac{3}{4} *\frac{5}{6}=\frac{15}{24}=\frac{5}{8}[/tex]
so now we have [tex]\frac{1}{5} + \frac{5}{8}[/tex] in order to add these to fractions together, there needs to be a common denominator. The easiest way to get this by multiplying the denominators by each other
[tex]\frac{1}{5} *\frac{8}{8}=\frac{8}{40}[/tex] and [tex]\frac{5}{8} * \frac{5}{5} = \frac{25}{40}[/tex] we can do this because anything times 1 is itself and [tex]\frac{5}{5} =\frac{1}{1}[/tex] and [tex]\frac{8}{8} =\frac{1}{1}[/tex]
now that we have common denominators we can add them together
[tex]\frac{8}{40} +\frac{25}{40} =\frac{33}{40}[/tex] depending on what your teacher wants you can leave it as a fraction or just type it into a calculator to get a decimal.
