Simplify:
#3/5 xx (-1/4-1/6) -:(-7/3+5/4)#
Follow the order of operations: parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.
Simplify the parentheses first.
#(-1/4-1/6)# must have a common denominator. The least common denominator (LCD) can be found by listing the multiples of #4# and #6#.
#4:##4,8,color(red)12,16...#
#6:##6,color(red)12...#
LCD#=##color(red)12#
Multiply both fractions by a fraction equal to #1#, so that each will have the same denominator. For example, #5/5=1#. This way, the values don't change.
#(-1/4xxcolor(teal)3/color(teal)3-1/6xxcolor(magenta)2/color(magenta)2)#
Simplify.
#(-3/12-2/12)=(-5/12)#
Return #(-5/12)# to the original expression.
#3/5 xx (-5/12) -:(-7/3+5/4)#
Simplify #(-7/3+5/4)#.
Follow the same procedure as with #(-1/4-1/6)#.
LCD#=##12#
#(-7/3xxcolor(green)4/color(green)4+5/4xxcolor(red)3/color(red)3)#
Simplify.
#(-28/12+15/12)=-13/12#
Return #(-13/12)# to the original equation.
#3/5 xx (-5/12) -:(-13/12)#
Multiply #3/5# and #-5/12#.
#-15/60-:(-13/12)#
Divide #-15/60# and #-13/12#.
When dividing by a fraction, invert the fraction and multiply.
#-15/60xx-12/13#
Simplify.
#180/780#
Reduce by dividing the numerator and denominator by #60#.
#(180-:60)/(780-:60)=3/13#
