Simplify the aritmetic expression: #[3/4 ·1/4 ·(5− 3/2)-: (3/4 − 3/16)] -: 7/4 ·(2 + 1/2)^2 −(1 + 1/2)^2#?
1 Answer
Explanation:
Given,
#[3/4*1/4*(5-3/2)-:(3/4-3/16)]-:7/4*(2+1/2)^2-(1+1/2)^2#
According to B.E.D.M.A.S., start by simplifying the round bracketed terms in the square brackets.
#=[3/4*1/4*(color(blue)(10/2)-3/2)-:(color(blue)(12/16)-3/16)]-:7/4*(2+1/2)^2-(1+1/2)^2#
#=[3/4*1/4*(color(blue)(7/2))-:(color(blue)(9/16))]-:7/4*(2+1/2)^2-(1+1/2)^2#
Omit the round brackets in the square brackets.
#=[3/4*1/4*7/2-:9/16]-:7/4*(2+1/2)^2-(1+1/2)^2#
Simplify the expression within the square brackets.
#=[3/16*7/2-:9/16]-:7/4*(2+1/2)^2-(1+1/2)^2#
#=[21/32*16/9]-:7/4*(2+1/2)^2-(1+1/2)^2#
#=[(21color(red)(-:3))/(32color(purple)(-:16)) * (16color(purple)(-:16))/(9color(red)(-:3))]-:7/4*(2+1/2)^2-(1+1/2)^2#
#=[7/2*1/3]-:7/4*(2+1/2)^2-(1+1/2)^2#
#=[7/6]-:7/4*(2+1/2)^2-(1+1/2)^2#
Omit the square brackets since the term is already simplified.
#=7/6-:7/4*(2+1/2)^2-(1+1/2)^2#
Continue simplifying the terms in the round brackets.
#=7/6-:7/4*(4/2+1/2)^2-(2/2+1/2)^2#
#=7/6-:7/4*(5/2)^2-(3/2)^2#
#=7/6-:7/4*(25/4)-(9/4)#
Omit the round brackets since the bracketed terms are already simplified.
#=7/6-:7/4*25/4-9/4#
#=7/6*4/7*25/4-9/4#
The
#=color(red)cancelcolor(black)7/6*color(purple)cancelcolor(black)4/color(red)cancelcolor(black)7*25/color(purple)cancelcolor(black)4-9/4#
#=25/6-9/4#
Change the denominator of each fraction such that both fractions have the same denominator.
#=25/color(red)6(color(purple)4/color(purple)4)-9/color(purple)4(color(red)6/color(red)6)#
#=100/24-54/24#
#=46/24#
#=23/12#
