Question 1089498
I would write it as
7/3÷[4/3+(4/3×16/5-16/5)]×9/5
because the outside parentheses are not needed,
and in 7th grade they taught me that
the innermost parenthesis are curvy ones,
the set around them is square parentheses,
and the next one is the curly ones.
Because I see slashes and division signs,
I would read 4/3×16/5 as {{{(4/3)*(16/5)}}} ,
but it would mean the same if I read it as 4÷3×16÷5 .
 
I see to ways to calculate that.
 
THE JUST CALCULATE WAY:
(I will keep using the symbols ÷ and × until it gets impractical)
7/3÷[4/3+(4/3×16/5-16/5)]×9/5=
7/3÷[4/3+(64/15-16/5)]×9/5=
7/3÷[4/3+(64/15-48/15)]×9/5=
7/3÷(4/3+16/15)×9/5=
7/3÷(20/15+16/15)×9/5=
7/3÷(36/15)×9/5=
7/3×(15/36)×9/5=
{{{7*15*9/(3*36*5)}}}=
{{{7*(3*5)*9/(3*(4*9)*5)}}}=
{{{7*3*5*9/(3*4*9*5)}}}=
{{{7*cross(3)*cross(5)*cross(9)/(cross(3)*4*cross(9)*cross(5))}}}={{{7/4}}}
I could have multiplied to get
{{{7*15*9/(3*36*5)=945/540}}} and then tried to simplify,
but I prefer to simplify early and often.
It is easier (at least for me).
 
APPLYING THE DISTRIBUTIVE PROPERTY:
{{{7/3}}}{{{"÷"}}}{{{"["}}}{{{4/3}}}{{{"×"}}}{{{"("}}}{{{16/5}}}{{{"-"}}}{{{16/5}}}{{{")"}}}{{{"]"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{"["}}}{{{4/3}}}{{{"+"}}}{{{(4/3-1)}}}{{{"×"}}}{{{16/5}}}{{{"]"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{"("}}}{{{4/3}}}{{{"+"}}}{{{1/3}}}{{{"×"}}}{{{16/5}}}{{{")"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{"["}}}{{{1/3}}}{{{"×"}}}{{{"("}}}{{{4}}}{{{"+"}}}{{{16/5}}}{{{")"}}}{{{"]"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{"["}}}{{{1/3}}}{{{"×"}}}{{{"("}}}{{{20/5}}}{{{"+"}}}{{{16/5}}}{{{")"}}}{{{"]"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{"("}}}{{{1/3}}}{{{"×"}}}{{{36/5}}}{{{")"}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"÷"}}}{{{12/5}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"×"}}}{{{5/12}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7/3}}}{{{"×"}}}{{{5/12}}}{{{"×"}}}{{{9/5}}}{{{"="}}}
{{{7*cross(5)*9/(3*12*cross(5))=7*9/(3*12)=7*3*3/(3*3*4)=7*cross(3)*cross(3)/(cross(3)*cross(3)*4)=7/4}}}