How do you simplify #2/3times7/2div(9/4+3/5)#?

#\frac{\cancel 2}{3}\cdot\frac{7}{\cancel 2}\div(\frac{9}{4}+\frac{3}{5})#
#=\frac{7}{3}\div(\frac{9\cdot 5}{4\cdot 5}+\frac{3\cdot 4}{5\cdot 4})#
#=\frac 7 3\div (\frac (45+12) 20)#
#=\frac 7 3\div \frac 57 20#
#=\frac 7 3\cdot \frac 20 57=\frac 140 171#

When multiplying fractions, just multiply the numerators (top numbers) together and then multiply the denominators (bottom numbers) together. Then cancel down if possible.

#2/3# x #7/2# =#14/6# = #7/3#

When adding/subtracting fractions they must have the same denominators. With denominators of 4 and 5 change them to equivalent fractions with a denominator of 20

#9/4# + #3/5# = #45/20# + #12/20#

=#57/20#

So #2/3# x #7/2 -: (9/4# + #3/5)# becomes

#7/3 -: (57/20)#

When you divide by a fraction you Keep Flip Change (KFC)
Keep the first fraction as it is
Flip the second fraction upside down
Change the divide sign to a multiply sign

#7/3# x #20/57# = #140/171#

#color(purple)(2/3xx7/2-:color(green)((9/4+3/5)))#

#color(blue)("Deal with the brackets first:")#

#color(green)([9/4color(red)(xx1)]+[3/5color(red)(xx1)] color(white)("ddd")->color(white)("ddd")[9/4color(red)(xx5/5)] +[3/5color(red)(xx4/4)])#

#color(green)(color(white)("ddddddddddddddddddd")->color(white)("dddddd") 45/20color(white)("dd")+color(white)("ddd")12/20 )#

#color(green)(color(white)("ddddddddddddddddddd")->color(white)("ddddddddddd")57/20 )#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all back together again")#

#color(purple)(2/3xx7/2-:57/20#

Multiply and divide have equal standing in importance of order. This is because it does not matter what order you do it in if they are next to each other. You get the same answer.

So we elect to work from left to right

#color(purple)(2/3xx7/2color(green)(-:57/20)#

#color(purple)(14/6)color(green)(-:57/20)#

Write as: #14/6xx20/57 = 140/171#