How do you evaluate #35- 5\times 2+ 9\div 3#?

We use #color(blue)(BODMAS)# to help simplify this. There are no Brackets and no Orders, so we go straight to Division and then Multiplication, before going on to Addition and then Subtraction. The direction is left to right.

#35-5xx2+9-:3#

There are no #color(blue)B#rackets and nor #color(blue)O#rders, so we go directly to Division.

There is one #color(blue)D#ivision: #9-:3=3#

Hence:

#35-5xx2+3#

Next comes #color(blue)M#ultiplication: #5xx2=10#

Hence:

#35-10+3#

Next comes #color(blue)A#ddition and #color(blue)S#ubtraction. Since they follow equally we move from left to right:

#35-10=25#

#25+3=28#

#28#

In calculating the value of an expression with different operations, always count the number of TERMS first - they are separated from each other by #+ and -# signs.

Each TERM simplifies to a single answer and these are added or subtracted in the last line.

Within each term, do Brackets, then powers and roots, then multiply and divide.

#color(blue)(35)color(red)(" "-" "5xx2" ")color(green)(+" "9div3)" "larr# there are 3 terms
#darrcolor(white)(wwww.ww)darrcolor(white)(www.www)darr#
#color(blue)(35)color(red)(" "-" "10" ")color(green)(+" "3)#

To avoid errors, it is a good idea to write all the additions first, then the subtractions:

#=color(blue)(35)" "color(green)(+" "3)color(red)(" "-" "10)#

#=28#