We want to multiply and divide some given fractions.
The general rules are:
For multiplication:
[tex]\frac{x}{y} *\frac{a}{b} = \frac{x*a}{y*b}[/tex]
For division:
[tex]\frac{x}{y} /\frac{a}{b} = \frac{x*b}{y*a}[/tex]
Now let's solve the given operations:
Multiplications:
[tex]\frac{2}{7} *\frac{1}{3} = \frac{2*1}{7*3} = \frac{2}{21}[/tex]
[tex]\frac{6}{11} *\frac{22}{30} = \frac{6*22}{11*30} = \frac{132}{330}[/tex]
[tex]\frac{1}{8} *32 = \frac{1}{8} *\frac{32}{1} = \frac{1*32}{8*1} = \frac{32}{8} = 4[/tex]
[tex](2 + 1/2)*(5 + 1/3) = 10 + \frac{5}{2} + \frac{2}{3} + \frac{1}{2*3} = 10 + \frac{20}{6}[/tex]
Divisions:
[tex]\frac{3}{4} /\frac{1}{3} = \frac{3*3}{4*1} = \frac{9}{4}[/tex]
[tex]\frac{6}{1} /\frac{1}{7} = \frac{6*7}{1} = 42[/tex]
[tex](4 + 7/8)/(3 + 1/4) = (\frac{4}{1} + \frac{7}{8} )/ (\frac{3}{1} + \frac{1}{4} ) = (\frac{4}{3} + \frac{4*4}{1*1} + \frac{7*1}{8*3} + \frac{7*4}{8*1} )\\= \frac{535}{24}[/tex]
[tex]11/\frac{1}{9} = \frac{11}{1} /\frac{1}{9} = \frac{11*9}{1*1} = 99[/tex]
If you want to learn more, you can read:
https://brainly.com/question/2885817
